The displacement from rest of a mass attached to a spring satisfies the simple harmonic motion equation x(t) = A cos(wt - o), where o is a phase constant, w is the angular frequency, and A is the amplitude. Find the average velocity, the average speed (magnitude of velocity), the average displacement, and the average distance from rest (magnitude of displacement) of the mass. average velocity average speed average displacement average distance from rest

What is the phase constant (from 0 to 2π rad) for the harmonic oscillator with the velocity function v(t) given in the figure if the position function x(t) has the form x = xmcos(wt + p)? The vertical axis scale is set by vs = 5.00cm/s. Number 1.57 v (cm/s) -15 Units rad

A particle moving along the x axis in simple harmonic motion starts from its equilibrium position, the origin, at t = 0 and moves to the right. The amplitude of its motion is 3.40 cm, and the frequency is 2.10 Hz. (a) Find an expression for the position of the particle as a function of time. (Use the following as necessary: t. Assume that x is in centimeters and t is in seconds. Do not include units in your answer.) X = (b) Determine the maximum speed of the particle. cm/s (c) Determine the earliest time (t > 0) at which the particle has this speed S (d) Find the maximum positive acceleration of the particle. cm/s² (e) Find the earliest time (t > 0) at which the particle has this acceleration. (f) Determine the total distance traveled between t = 0 and t = 0.71 s. cm

for the simple pendulum, the dependence of period T on the length L of the pendulum is?   a. T alpha L2 b.  T alpha square root L c. T independent of L d. T alpha L