Problem 12:  A mass m = 1.2 kg hangs at the end of a vertical spring whose top end is fixed to the ceiling. The spring has spring constant k = 145 N/m and negligible mass. At time t = 0 the mass is released from rest at a distance d = 0.35 m below its equilibrium height and undergoes simple harmonic motion with its position given as a function of time by y(t) = A cos(ωt – φ). The positive y-axis points upward. Enter an expression for the velocity along the y-axis as a function of time, in terms of A, φ, ω, and t.

Problem 5: A mass m = 1.81 kg hangs at the end of a vertical spring whose top end is fixed to the ceiling. The spring has spring constant k = 86 N/m and negligible mass. The mass undergoes simple harmonic motion when placed in vertical motion. At time t = 0 the mass is observed to be at a distance d = 0.55 m below its equilibrium height with an upward speed of vo = 4.1 m/s. Determine the phase angle of the motion, in radians. ) Determine the amplitude of the motion, in m. Determine the distance from equilibrium, in m, when the mass moves with a speed half its initial speed.

A particle with a mass of 3.4 x 1020 kg is oscillating with simple harmonic motion with a period of 3.5 × 10° s and a maximum speed of 4.3 x 10° m/s. Calculate (a) the angular frequency and (b) the maximum displacement of the particle. (a) Number Units (b) Number Units

The graph shows the x-displacement as a function of time for a particular object undergoing simple harmonic motion. This function can be described by the following formula:x(t) = Acos(ωt+φ)where x and A are measured in meters, t is measured in seconds, ω is measured in 1/s and φ is measured in radians. A=2.90m, T=4.00s, ω=1.57 1/s, f=2.50*10^-1 Hz Determine the phase constant i.e. find the smallest positive value for φ.

See attached picture, a 5 kilogram block is pressed against a spring compressing the spring by 25 centimeters. The spring constant is k = 4000 Newton/meters. If the block is released from rest at the bottom of a frictionless incline with an angle of 25 degrees, find how far up the incline the block will slide before stopping.

A 0.60 kg block rests on a frictionless horizontal countertop, where it is attached to a massless spring whose k-value equals 23.0 N/m. Let x be the displacement, where x = 0 is the equilibrium position and x > 0 when the spring is stretched. The block is pushed, and the spring compressed, until xi = −4.00 cm. It then is released from rest and undergoes simple harmonic motion. Have answer to a need answers to b-d (a)What is the block's maximum speed (in m/s) after it is released?  0.25 m/s (b) How fast is the block moving (in m/s) when the spring is momentarily compressed by 2.10 cm (that is, when  x = −2.10 cm)?  ____________________ m/s (c) How fast is the block moving (in m/s) whenever the spring is extended by 2.10 cm (that is, when passing through  x = +2.10 cm)?  _________________m/s (d) Find the magnitude of the displacement (in cm) at which the block moves with one-half of the maximum speed. |x| =  ___________________ cm

A simple harmonic oscillator consists of a mass m attached to a spring with spring constant k, with displacement given by x = A sin(wt + ¢) . Which one of the following is NOT true? O The frequency is independent of the amplitude O The potential energy is a maximum when (wt + 4) = 0 The kinetic energy is a maximum when (wt + ¢) = 0 O The restoring force must be proportional to the negative of the displacement O Increasing the mass will decrease the frequency

A mass on a spring, moving with simple harmonic motion, vibrates with a frequency of 4.0 Hz and an amplitude of 8.0 cm. If x = 8.0 cm when t = 0, find its speed when t = 3 s.

The functionx = (4.7 m) cos[(6πrad/s)t + π/3 rad]gives the simple harmonic motion of a body. At t = 7.4 s, what are the (a) displacement, (b) velocity, (c) acceleration, and (d) phase of the motion? Also, what are the (e) frequency and (f) period of the motion?