The motion of a body is described by the equation 1.65 sin (0.470πt) where t is in s and y is in m. (a) Find the amplitude. (b) Find the period. (c) Find the frequency. (d) Find the displacement at t = 3.50 s. (e) Find the displacement at t = 23.0 s.

The free-fall acceleration on the Moon's surface is g = 1.63 m/s². How long must a pendulum be to have a period of 3.5 seconds on the Moon? Enter the length in meters, without the unit. For full credit, your answer must be within ±2% of the correct value.

The position of an oscillating mass is given by x=[0.10m]cos(2.5t) where t is in seconds. What is the amplitude of the oscillation? 2.5m 0.04m 0.25m 0.10m

A spring is hanging down from the ceiling, and an object of mass m is attached to the free end. The object is pulled down, thereby stretching the spring, and then released. The object oscillates up and down, and the time T required for one complete up-and-down oscillation is given by the equation T = 2л√/m/k, where k is known as the spring constant. What must be the dimension of k for this equation to be dimensionally correct? O [T] O [T]² O [M] O [M]/[T] O [T]/[M] O [M]/[T]² O [T]²/[M]

A simple pendulum has a frequency of 0.400 [Hz] for small oscillations on the surface of the Earth. What is the period of the same pendulum on the surface of the moon, where g=g= 1.62 [m/s2]?

An oscillating block-spring system has a mechanical energy of 3.03 J, an amplitude of 7.40 cm, and a maximum speed of 4.95 m/s. Find (a) the spring constant, (b) the mass of the block and (c) the frequency of oscillation. (a) Number 81.89 (b) Number 0.018 (c) Number 10.65 Units N/m Units kg Units Hz

A simple pendulum makes 100 complete oscillations in 3.30 min at a location where g = 9.80 m/s2. (a) Find the period of the pendulum. s(b) Find the length of the pendulum. m

A simple pendulum has a length of 52.6 cm and makes 81.6 complete oscillations in 2.00 min. (a) Find the period of the pendulum. (b) Find the value of g at the location of the pendulum. m/s2

Problem 3: An object is undergoing simple harmonic motion along the x-axis. Its position is described as a function of time by x(t) = 1.7 cos(3.1t – 1.3), where x is in meters, the time, t, is in seconds, and the argument of the cosine is in radians. Part (a) Find the amplitude of the simple harmonic motion, in meters. Part (b) What is the value of the angular frequency, in radians per second? Part (c) Determine the position of the object, in meters, at the time t = 0. Part (d) What is the object's velocity, in meters per second, at time t = 0? Part (e) Calculate the object's acceleration, in meters per second squared, at time t = 0. Part (f) What is the magnitude of the object's maximum acceleration, in meters per second squared?

Problem #10: A pendulum with a period of 2.00000 s in one location (g=9.80m/s2) is moved to a new location where the period is now 1.99748 s. a) What is the acceleration due to gravity at its new location? (report your answer to at least 5 decimal places)