Show all working explaining detailly each step.Q(iii) (c) A mass m hangs on a string of length /from a rigid support. The mass is pulledaside, so that the string makes an angle 0with the vertical, and then released.(i) Show that the mass executesSHM, stating any assumptionsmade.(ii) Prove that the period T of thisSHM is given by T= 2n (iii) A student times a simple pendu-lum to determine T.Does it matterhow manyoscillatiohs are counted?Does it matter from whefe thecounts are taken - the end'or themiddle of the swing? Give reasons.

Answered: Image /qna-images/answer/ce0cdc4f-9885-4899-9496-d8b3fd9d872c.jpg

(iii) A student times a simple pendu- lum to determine T.Does it matter how manyoscillatiohs are counted? Does it matter from whefe the counts are taken - the end or the middle of the swing? Give reasons.

(iii) A student times a simple pendu- lum to determine T.Does it matter how manyoscillatiohs are counted? Does it matter from whefe the counts are taken - the end or the middle of the swing? Give reasons.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter15: Oscillations

Section: Chapter Questions

Problem 15.4CYU: Check Your Understanding An engineer builds two simple pendulums. Both are suspended from small...

See similar textbooks

Related questions

Q: What is elastic after effect?

A: When a substance is stretched and after removal of deforming force material takes time to regain its…

Q: The amplitude of a simple harmonic oscillator is doubled, How does it affect the total energy?

A: Relation between the total energy and amplitude is given as:

Q: At what positions of the simple pendulum its (a) PE is maximum (b) KE is zero?

A: (a) Write the expression for the potential energy (PE) for the pendulum.

Q: A tire swing hanging from a branch reaches nearly to the ground (Fig. 11–49). How could you estimate…

A: The tire swing hanging from a branch of a tree, it will be oscillate like a simple pendulum. The…

Q: Most harmonic oscillators are damped and, if undriven, eventually come to a stop. Why?

A: Most harmonic oscillators are damped, if undriven, eventually comes to rest.

Q: In an engine, a piston oscillates with simple harmonic motion so thát its position varies according…

A: (a) Oscillation relation of a piston executing simple harmonic motion xt=3.00 cmcos5t+π7 At t=0…

Q: frequency ff′ of the oscillatio

Q: Will damped oscillations occur for any values of b and k? Explain.

A: The angular frequency of damped oscillations,

Q: Slug mass equal (1/4) is hungged on to a spring, whereupon the spring is stretched 1/2 ft from its…

Q: The chemical bond between the two atoms in a diatomic oxygen molecule acts very much like aspring,…

Q: A point on a rotating disc is not considered to be simple harmonic ,Why?

A: In simple harmonic motion the acceleration of the body executing the motion will be proportional to…

Q: A simple pendulum of length L and mass M gas frequency f, to increase it's frequency to 2f?

Q: A0.55 K9-mass Suse harmonic OSCIllation the period to 2.25s Am - ?

Q: A pendulum bob swings through an arc 40 cm long on its first swing. Each swing thereafter, it swings…

A: For the first swing the distance =40cmthe second swing the distance =0.8×40cmthe third swing the…

Q: A massless spring of constant 4ON/m is attached vertically to a table. A 5-g balloon is filled with…

A: Net force stretching the spring upwards = bouyancy force - weight of baloon Net force stretching the…

Q: A mass attached to a spring vibrates with a natural frequency of 20 C/s while its frequency for…

A: Natural frequency = 20c/s Frequency for damped vibrations= 16c/s

Q: The energy of the simple harmonic oscillator is given by the relationship E=nhw.

A: E =nhw is energy defined for photon like particle In the case of Simple Harmonic oscillator, energy…

Q: Suppose that a swing takes 4.991 s to complete one cycle. What is the swing’s period?

A: Given data *The swing takes time to complete one cycle is t = 4.991 s *The swing complete one cycle

Q: A pendulum of mass 50 gm and length 90 cm is left to swing from an intial angle of 30 degrees, and…

Q: a pan of mass mp = 0.2 kg is susper mm = 2.2 kg is dropped onto the meat makes a totally inelastic…

A: Givenk=400 N/mmp=0.2 kgmm=2.2 kgh=0.4 m

Q: show that the following furcton is harmonic: Sin x

A: Given: Function, e-ysinx

Q: A massless spring of constant 40N/m is attached vertically to a table. A 5-g balloon is filled with…

A: time period =mk

Q: A certain mass hanging from a string of length L has a period of oscillation, Tpend. The same mass…

Q: Coupled Flarmonic Oscillators X2 : 0 ) Write down the 2nd law for each of the masses. Use…

A: We will only answer the first question since the exact question to be answered was not specified.…

Q: A parhicle of under the 4 mass m' the of VO)-(1-ax)e Determine moves. patential energy X20 and gian…

A: A system is said to be in equilibrium if the net force on the system is zero. There are three…

Q: Because of dissipative forces, the amplitude of an oscillator decreases 3.96% in 10 cycles. By what…

Q: (II) If one oscillation has 3.0 times the energy of a secondone of equal frequency and mass, what is…

Q: Because of dissipative forces, the amplitude of an oscillator decreases 4.94% in 10 cycles. By what…

A: Introduction: Spring motion is the examples of simple harmonic motion where body passes through a…

Q: Example 21.44. A particle of mass m can oscillate about the position of equilibrium under the effect…

Q: A 7-kg mass is hung from the bottom end of vertical of a vertical spring fastened to an overhead…

A: Given: Mass hanged (m) = 7 kg. Period (T) = 2.6 s.

Q: Consider a damped harmomic oscillater 0'05kg and for which K is 5o Nm: State and sketch the nature…

A: The angular frequency for a damped harmonic oscillator can be expressed by the following equation.…

Q: 1. If you hold the mass at the spring's equilibrium what kind of energy would it posses?

Q: RI 2F 2ft イRe

Q: Most harmonic oscillators are damped and, if undriven, eventually come to a stop. How is this…

A: How is this damped oscillation related to the second law of thermodynamics?

Q: - find the frequeny of osullation of a pendulum'of air resistance and weignt of rod, and assuning o…

A: We have given pendulum of length L and we need to find frequency of oscillation. For which we need…

Q: Could the same result be achieved by the motion of self-interstitials?

A: Movement of atoms in crystal is due to motion of vacancies and same result can be achieved by…

Q: (II) A 1.65-kg mass stretches a vertical spring 0.215 m. Ifthe spring is stretched an additional…

A: We Use the equation of period of oscillation for a mass 'm' on the end of the spring to calculate…

Q: A horizontal spring-mass system oscillates on a frictionless table. If the ratio of the mass to the…

Question

Show all working explaining detailly each step.

Q(iii)

(c) A mass m hangs on a string of length /
from a rigid support. The mass is pulled
aside, so that the string makes an angle 0
with the vertical, and then released.
(i) Show that the mass executes
SHM, stating any assumptions
made.
(ii) Prove that the period T of this
SHM is given by T= 2n

(iii) A student times a simple pendu-
lum to determine T.Does it matter
how manyoscillatiohs are counted?
Does it matter from whefe the
counts are taken - the end'or the
middle of the swing? Give reasons.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

Check Your Understanding Why are completely undamped harmonic oscillators so rare?
Find the frequency of a tuning fork that takes 2.50103 s to complete one oscillation.
Two parakeets sit on a swing with their combined CMs 10.0 cm below the pivot. At what frequency do they swing?
. A mass of 0.75 kg is attached to a relaxed spring with k = 2.5 N/m. The mass rests on a horizontal, frictionless surface. If the mass is displaced by 0.33 m, what is the magnitude of the force exerted on the mass by spring? If the mass is then released to execute simple harmonic along the surface, with what frequency will it oscillate?
Give an example of a simple harmonic oscillator, specifically noting how its frequency is independent of amplitude.
Check Your Understanding The wave function above is derived using a sine function. Can a cosine function be used instead?
Parcels of air (small volumes of air) in a stable atmosphere (where the temperature increases with height) can oscillate up and down, due to the restoring force provided by the buoyancy of the air parcel. The frequency of the oscillations are a measure of the stability of the atmosphere. Assuming that the acceleration of an air parcel can be modeled as 2zt2=g(z)0zz , prove that z=z0etN2 is a solution, where N is known as the Brunt-Väisälä frequency. Note that in a stable atmosphere, the density decreases with height and parcel oscillates up and down.
A mass m0is attached to a spring and hung vertically. The mass is raised a short distance in the vertical direction and released. The mass oscillates with a frequency f0. If the mass is replaced with a mass nine times as large, and the experiment was repeated, what would be the frequency of the oscillations in terms of f0?
Check Your Understanding An engineer builds two simple pendulums. Both are suspended from small wires secured to the ceiling of a room. Each pendulum hovers 2 cm above the floor. Pendulum 1 has a bob with a mass of 10 kg. Pendulum 2 has a bob with a mass of 100 kg. Describe how the motion of the pendulums will differ if the bobs are both displaced by 12°.
A pendulum clock works by measuring the period of a pendulum. In the springtime the clock runs with perfect time, but in the summer and winter the length of the pendulum changes. When most materials are heated, they expand. Does the clock run too fast or too slow in the summer? What about the winter?
Consider a place where the gravity is 4 times the gravity on Earth (g' 4g), then %3D the frequency of oscillation of a simple pendulum in that place, f', as compared to its frequency on earth is:
3) A small sphere has radius 2cm and mas 60g. It is suspended at equilibrium from a spring with spring 14 w/m! Find how much the sphore shetches the stored in the spring. Constand and Spring the energy ^ i's pulled down an b From equilibrium, the sphere addinord Bem and released so it oscillates. up and down harmonically. Alse conservation of energy to calculate the kinetic energy to the equilibrium height. the sphere when it returns 18