6. Calculate the frequency of the compound pendulum shown below by using the energy method if a mass mT is added to the tip. //// g MT //
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- rad The rod OA rotates clockwise at a constant angular velocity of 0 = (3) Two pin-connected slider block, located at B, move freely on OA. The curved rod is described by the equation r (300 (3-cos)) m. Hint: 1. Remember clockwise rotation is negative velocity. OA Variable 0₁ d₁ d₂ d3 0₁ d2 d3 Values for the figure are given in the following table. Note the figure may not be to scale. Value 110 degrees 0.45 m 0.1 m 0.275 m Using cylindrical components, a. Determine the cylinders's radial and transverse components of velocity at the instant shown, u, and vg. b. Determine the cylinders's radial and transverse components of acceleration at the instant shown, ar and ag. c. Determine the cylinder's magnitude of the velocity at the instant shown, ·M. d. Determine the cylinder's magnitude of the acceleration at the instant shown, |a1. Round your final answers to 3 significant digits/figures. 7= fr + a= M-C Hr+ m S M 82 He) Fe) m S m(The complete question is in the picture) Consider a 2.0 [kg] box that is attached to two identical springs that are in their relaxed state when the block is centered on the frictionless horizontal floor. The box is pressed to the left and then was released from rest as shown in the figure. If work done by the left spring is Wby spring = 25 [J], what is the speed of the boxas it passes the center x = 0? A. 8.2 [m/s]B. 7.1 [m/s]C. 3.5 [m/s]D. zeroUsing either Graphical Analysis or graph paper, plot a graph of pendulum period T vs. lengthl. Scale each axis from the origin (0,0). Does the period appear to depend on length?
- In an oscillatory motion of a simple pendulum, the ratio of the maximum angular acceleration, O"max, to the maximum angular velocity, O'max, is TI S^(-1). What is the time needed for the pendulum to complete one-half oscillation? O 0.25 sec O 0.5 sec O 2 sec O 4 sec O 1 sec A traveling wave on a taut string with a tension force T. is given by the wave noters and t is in1. A machine component of 2.25kg mass moves with SHM ,the amplitude being [MAX displ] 380mm.If it makes 120 oscillations per minute find the maximum acceleration and the accelerating force when the displacement is 250mm from mid-travel..A four-bar mechanism is used to transmit power to slider E. Link AC rotates counterclockwise at 100 rpm. A and B are fixed points. The following linkages are measured in cm: AC=35, AB=70, CD=45, BD=45, DE=40. Find the instantaneous velocity of slider E in cm/s 1.Draw the mechanism in appropriate scale on your paper2. Find the instantaneous linear velocity of C3. Find a point on your paper to draw the velocity polygon and scale the magnitude of the computed linearvelocity4. Use the relative velocity equation for finding the linearvelocity of D; ? = ? + ?? ? ?/?5. Remember that although the magnitudes are unknown, their directions can be identified6. Obtain the magnitudes of the unknown velocities from the velocity polygon7. For Link DE, repeat the process by using ? = ? + ??the line as much as needed8. Remember that E is a SLIDER therefore it can only goin the direction where its movement is not constrained? . Add the vector ? to the head of ? and extend?/? ?/??
- Question 1 A sketch of a valve and rocker arm system for an internal combustion engine is give in below figure. Model the system as a pendulum attached to a spring and a mass. Determine the equations of motion and calculate the natural frequency in rad/s. The mass moment of inertia of the rocker arm about its pivot point j=0.46, the stiffness of the valve springspring k=420 , the distance from pivot to spring I= 0.98 m, and the mass of the valve m=3.2 kg. Ignore the mass of the spring and the oil effect. Rocker arm Follower k Valve spring LOil Cam m Valve• A 1 kg mass is attached to 0.5 meter string. What is the cycle period of oscillation for the mass when it moves as a simple pendulum. If the mass is increased to 2 kg, what is the period, T? Gravity 8 //// 0 [= length mFind the amplitude, frequency and period of motion for an object vibrating at the end of a horizontal spring if the equation for its position as a function of time is x=(0.250m) cos(π800t) a. Find the maximum magnitude of the velocity and acceleration. b. What is the position, velocity and acceleration of the object after 100s has elapsed?
- Vibrations Engineering: Mass = 10 kilogramsSpring constant = 400 Newtons per meterPeriodic Force = 6 NewtonsForcing Frequency = 5 radians per secondInitial Displacement = 80 millimetersInitial Velocity = 2 meters per second Calculate: (Express the final answer in 4 significant digits) -the constant B (in millimeters) for the complementary solution -the magnification factor of the vibration -the constant A (in millimeters) for the complementary solutionA spring is stretched 30cm by a mass of 2kg, and the mass is attached to a viscous damper that exerts a force of 6N when the velocity of the mass is 2m/s. a.) Find the differential equation that characterizes u(t), the displacement of the mass from equilibrium t, when it is set in motion. Specify the units that you are using and show find the parameters in the equation. You do not need to solve the equation here. how you b.) Find a fundamental pair of solutions for the equation you found in part a. c.) The mass is pulled down 40cm from the equilibrium and then thrust downwards with an initial speed of 2m/s. Find u(t).1. Express the angular resonant frequency for each of the undamped mechanical oscillating systems below: M TITT M M M (a) fuim-min (b) Fam-inf (c) (d)