Question

5. Given an equation of a 1.5 kg mass in SHM V=2.50 cos (0.25 t) , m/s Find a) the units on the values 2.50 and 0.25 b) the amplitude, angular frequency, frequency and period of this oscillation c) the displacement and the acceleration at t=2.00 seconds d) the stiffness of the spring supporting this oscillating mass

Answer 1

Ans: 1) The units on 2.50 is m/s and units on 0.25 is rad/s

2) Here,

  

- da d1 = 2.50 cos 0.25

>> = 2.50 esin 0.25t+c= 10 sin 0.25t + c 0.25

At t=0, x=0 => c=0.

r = 10 sin 0.25t = Asin wt

The amplitude of oscillations is 10 m

The angular frequency is 0.25 rad/s

  The frequency is

0.25 272x312=0.040H

The time period is

  

T-1_1 f 0.040 = 25.133

c) The displacement at t=2.00s is

I = 10 sin 0.25 x 2.00) = 4.794 m

The acceleration is

> a= = -0.625 sin 0.25t = -0.625 sin 0.25 x 2.00 = 0.3 m/s2

d) The stiffness of the spring is

k = mw2 = 1.5 x 0.25% = 0.09375 N/m