Question

An object is oscillating as depicted in the expression below. What is the period T ? Assume that the units work out and the amplitude is in millimeters and the time t t is in units of seconds. x ( t ) = sin ( π 10 t )
A. 110s
B. π5s
C. π10s
D. 10s
E. 20s

Answer 1

Answer:

The time period of the object is 0.2 seconds.

Explanation:

An object is oscillating as depicted in the expression below :

$x(t)=\sin (\pi 10t)$ ........(1)

The general equation is given by :

$x(t)=A\ \sin \omega t$  .......(2)

Comparing equation (1) and (2) we get :

$\omega=10\ \pi$

The relation between angular frequency and time period is given by :

$T=\dfrac{2\pi }{\omega}\\\\T=\dfrac{2\pi }{10\pi}$

T = 0.2 seconds

So, the time period of the object is 0.2 seconds.