A block of mass m = 2 kg connected to a spring completes one oscillation every three seconds. The motion has an amplitude of A = 3 m. The motion is started by pulling the mass to the right and then releasing it from rest. (a) Determine the spring constant of the spring. (b) What is the maximum acceleration of the block?

Multiple-Concept Example 6 presents a model for solving this problem. As far as vertical oscillations are concerned, a certain automobile can be considered to be mounted on four identical springs, each having a spring constant of 1.28 x 105 N/m. Then, four identical passengers are seated in the car, and it is set into a vertical oscillation that has a period of 0.387 s. If the mass of the empty car is 1560 kg, determine the mass of each passenger. Assume that the mass of the car and its passengers is distributed evenly over the springs.

A spiral staircase winds up to the top of a tower in an old castle. To measure the height of the tower, a rope is attached to the top of the tower and hung down the center of the staircase. However, nothing is available with which to measure the length of the rope. Therefore, at the bottom of the rope a small object is attached so as to form a simple pendulum that just clears the floor. The period of the pendulum is measured to be 6.10 s. What is the height of the tower? Number Units

A mass-spring system oscillates with an amplitude of 4.00 cm. If the spring constant is 241 N/m and the mass is 472 g, determine the mechanical energy of the system. Determine the maximum speed of the object. Determine the maximum acceleration.

A spring is mounted vertically on the floor. The mass of the spring is negligible. A certain object is placed on the spring to compress it. When the object is pushed further down by just a bit and the released, one up/ down oscillation cycle occurs in 0.230s. However, when the object is pushed by 5.32 x 10-2 m from unstrained position to point P and then released, the object flies entirely off the spring. To what height above point P does the object rise in the absence of air resistance?

A mass of 8.0 kg hangs from a spring attached to the ceiling. The spring has a spring constant of 500 N/m and it stretches 15.7 cm from its mean position. A student grabs the spring, applies a force and stretches it a further 6.7 cm downwards. The block is released and initially accelerates upward before undergoing simple harmonic motion. Calculate the initial vertical acceleration of the mass. (Units: m/s? , to 2 sig figs)

You pull a simple pendulum 0.240 m long to the side through an angle of 3.50° and release it. (a) How much time does it take the pendulum bob to reach its highest speed? (b) How much time does it take if the pendulum is released at an angle of 1.75° instead of 3.50°?

A spiral staircase wind up to the top of the tower in an old castle. To measure the height of the tower, a rope is attached to the top of the tower and hung down the center of the staircase. However, nothing is available with which to measure the length of the rope. Therefore, at the bottom of the rope a small object is attached so as to form a simple pendulum that just clears the floor. The period of the pendulum is measure to be 6.53 s. What is the height of the tower?

A 200 g mass is attached to a spring with k = 60 N/m and allowed to oscillate with an amplitude of 0.12 m.  What is the maximum speed of the mass?

Aweight is attached to a spring and is suspended from a ceiling so that it lies 30 cm from the ceiling when it is at rest. The spring is stretched so that the weight is 38 cm from the ceiling and is then released. It bounces up and down for a while. Each time it comes to the bottom of its bounce, the length of the stretch is 75% of the previous stretch. a) The period of each oscillation (bounce) is 1/2 second. Write an equation that represents the distance from the weight to the ceiling. b) Draw a graph of the function. c) Without doing any calculations, state the distance of the spring from the ceiling after 1 minute