A 064 kg mass is attached to the end of a spring and set int

A 0.64 kg mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a compressed position. The record of time is started when the oscillating mass passes through the equilibrium position and the position of the mass at any time is shown in the drawing. Determine the following. amplitude A of the motion m angular frequency ? rad/s spring constant k N/m speed of the object at t - 2.00 s magnitude of the object\'s acceleration at t = 2.00 s m/s^2

Solution

a) A = 0.9 m ( max value of X )

b) angular frequency = 2pi/T = 2*3.14)/(8 = 0.785 Hz

c) W = sqrt (k/m)

k = mW^2 = 0.64*0.785^2 = 0.394 N/m

d) speed at t= 2

= 0 ( as at X max V = min = 0)

e) a = W^2A at X max

=> a = 0.785^2*0.9 = 0.554 m/s^2