Question

A mass is vibrating at the end of a spring with a spring constant 1.14 N/m. The figure shows a graph of its position x (in centimetres) as a function of time t (in seconds).

A) At what time between t=0 s and the first maximum after t=0 s is the mass not moving?

B) What is the magnitude of the acceleration of the object at the second maximum in the x-t curve after t = 0 s?

C) What is the mass of the object?

D) How much energy did the system originally contain?

E) How much energy did the system lose between t = 0 s and the third maximum after t = 0 s? Think about where this energy has gone.

Answer 1

a] Object's velocity becomes zero at extreme positions (maximum or minimum )

Within he given interval, objet is not moving at t = 0.8s

b]acceleration a = w^2x = (2pi/T)^2*x = [2pi/1.6]^2 *0.032 = 0.4935 m/s^2

c] We have k/m = w^2

m = k/w^2

= 1.14/[2pi/1.6]^2

= 0.07392 kg

d] Initial energy = 0.5kx^2 = 0.5*1.14*0.06^2 = 0.002052 J

e] Energy lost = initial energy - final energy = 0.5kx0^2 - 0.5kx3^2 = 0.5*1.14*0.06^2 - 0.5*1.14*0.022^2

= 0.001776 J