mass, m www www x(t) = F Figure 1: Mass spring system approximation of car 2. A car with an effective mass of 1000kg can be approximated by the spring mass system shown in Figure 1 and has a damping ratio of 0.5. Each spring has a spring www stiffness of 10kN/m. Two people get into the car simultaneously at time 0, and each person weighs 70kg. Given that the resulting displacement from a step load F at time T is given by Equation 2. -{wn (t-T) COS = [walt-T) -7) – tan-¹ k√/₁-8²² (a) Calculate the time at which displacement is maximum (b) Calculate the maximum displacement (c) The value of displacement at time t → ∞ vie] t

The expression x = 8.50 cos (2.40 t + /2) describes the position of an object as a function of time, with x in centimeters and t in seconds. What are the a. frequency, b. period, c. amplitude, and d. initial phase of the objects motion? e. What is the position of the particle at t = 1.45 s?

(a) If frequency is not constant for some oscillation, can the oscillation be SHM? (b) Can you think of any examples of harmonic motion where the frequency may depend on the amplitude?

A spring has a length of 0.200 m when a 0.300kg mass hangs from it, and a length of 0.750 m when a 1.95-kg mass hangs from it. (a) What is the force constant of the spring? (b) What is The unloaded length of the spring?

Table P16.59 gives the position of a block connected to a horizontal spring at several times. Sketch a motion diagram for the block. Table P16.59

Consider the position data for the block given in Table P16.59. What are the signs of the blocks velocity and acceleration at the first five times listed?

A 0.250-kg block along a horizontal track has a speed of 1.50 m/s immediately before colliding with a light spring of force constant 4.60 N/m located at the end of the track. (a) What is the springs maximum compression if the track is frictionless? (b) If the track is not frictionless, would the springs maximum compression be greater than, less than, or equal to the value obtained in part (a)?

(a) What is the effect on the period of a pendulum if you double its length? (b) What is the effect on the period of a pendulum if you decrease its length by 5.00%?

In the short story The Pit and the Pendulum by 19th-century American horror writer Edgar Allen Poe, a man is tied to a table directly below a swinging pendulum that is slowly lowered toward him. The bob of the pendulum is a 1-ft steel scythe connected to a 30-ft brass rod. When the man first sees the pendulum, the pivot is roughly 1 ft above the scythe so that a 29-ft length of the brass rod oscillates above the pivot (Fig. P16.39A). The man escapes when the pivot is near the end of the brass rod (Fig. P16.39B). a. Model the pendulum as a particle of mass ms 5 2 kg attached to a rod of mass mr 5 160 kg. Find the pendulums center of mass and rotational inertia around an axis through its center of mass. (Check your answers by finding the center of mass and rotational inertia of just the brass rod.) b. What is the initial period of the pendulum? c. The man saves himself by smearing food on his ropes so that rats chew through them. He does so when he has no more than 12 cycles before the pendulum will make contact with him. How much time does it take the rats to chew through the ropes? FIGURE P16.39

A small ball is tied to a string and hung as shown in Figure P8.34. It is released from rest at position 1, and, during the swing, the string meets a fixed peg as shown. Explain why position 2 at which the ball comes momentarily to rest must be at the same height as position 1.