A block attached to a spring with unknown spring constant oscillates with a period of 2.00 s. What is the period if a. The mass is doubled? b. The mass is halved? c. The amplitude is doubled? d. The spring constant is doubled? Parts a to d are independent questions, each referring to the initial situation.

An oscillator with a mass of 500 g and a period of 0.50 s has an amplitude that decreases by 2.0% during each complete oscillation. If the initial amplitude is 10 cm, what will be the amplitude after 25 oscillations?

A 507 g mass oscillates with an amplitude of 10.0 cm on a spring whose spring constant is 20.0 N/m. Determine: a. The period. b. The maximum speed. c. The total energy.

a. When the displacement of a mass on a spring is $\frac{1}{2}A$ , what fraction of the energy is kinetic energy and what fraction is potential energy? b. At what displacement, as a fraction of A, is the energy half kinetic and half potential?

A heavy steel ball is hung from a cord to make a pendulum. The ball is pulled to the side so that the cord makes a $5 ^ { \circ }$ angle with the vertical. Holding the ball in place takes a force of 20 N. If the ball is pulled farther to the side so that the cord makes a $10 ^ { \circ }$ angle, what force is required to hold the ball?

A ball of mass m oscillates on a spring with spring constant k = 200 N/m. The ball's position is x = (0.350 m) cost (15.0 t), with t measured in seconds. a. What is the amplitude of the ball's motion? A. 0.175 m B. 0.350 m C. 0.700 m D. 7.50 m E. 15.0 m b. What is the frequency of the ball's motion? A. 0.35 Hz B. 2.39 Hz C. 5.44 Hz D. 6.28 Hz E. 15.0 Hz c. What is the value of the mass m? A. 0.45 kg B. 0.89 kg C. 1.54 kg D. 3.76 kg E. 6.33 kg d. What is the total mechanical energy of the oscillator? A. 1.65 J B. 3.28 J C. 6.73 J D. 10.1 J E. 12.2 J e. What is the ball's maximum speed? A. 0.35 m/s B. 1.76 m/s C. 2.60 m/s D. 3.88 m/s E. 5.25 m/s

A 200 g air-track glider is attached to a spring. The glider is pushed 10.0 cm against the spring, then released. A student with a stopwatch finds that 10 oscillating take 12.0 s. What is the spring constant?

A mass on a string of unknown length oscillates as a pendulum with a period of 4.00 s. What is the period if a. The mass is doubled? b. The string length is doubled? c. The string length is halved? d. The amplitude is halved? Parts a to d are independent questions, each referring to the initial situation.

A block with a mass of $0.28 \mathrm{~kg}$ is attached to a horizontal spring. The block is pulled back from its equilibrium position until the spring exerts a force of $1.0 \mathrm{~N}$ on the block. When the block is released, it oscillates with a frequency of $1.2 \mathrm{~Hz}$. How far was the block pulled back before being released?

Hummingbirds may seem fragile, but their wings are capable of sustaining very large forces and accelerations. as we discussed earlier shows data for the vertical position of the wing tip of a rufous hummingbird. What is the maximum acceleration of the wing tips, in m/s2 and in units of g?

a. When the displacement of a mass on a spring is $\frac { 1 } { 2 } A$, what fraction of the mechanical energy is kinetic energy and what fraction is potential energy? b. At what displacement, as a fraction of A, is the energy half kinetic and half potential?

The position of a 50 g oscillating mass is given by x(t) = (2.0 cm) cos (10 t), where t is in seconds. Determine: a. The amplitude. b. The period c. The spring constant d. The maximum speed. e. The total energy. f. The velocity at t = 0.40 s.

An air-track glider attached to a spring oscillates between the 10 cm mark and the 60 cm mark on the track. The glider completes 10 oscillations in 33 s. What are the (a) period, (b) frequency. (c) amplitude, and (d) maximum speed of the glider?

A block oscillating on a spring has a maximum speed of 20 cm/s. What will the block's maximum speed be if the total energy is doubled? Explain.