First slide

Simple harmonic motion

Question

The displacement of a particle is represented by the equation $y = 5 \cos (\frac{3 π}{2} - 2 π t)$ where y is displacement $ω$ is angular frequency in metre and t is given in instant of time in h the motion of the particle is

Moderate

A

simple harmonic with period of 1-hour
B

simple harmonic with a time period of $(\frac{2 π}{ω}) s$
C

periodic but not simple harmonic
D

simple harmonic with time period of $(\frac{2 π}{ω}) s$

Solution

The equation $y = 5 \cos (\frac{3 π}{2} - 2 π t)$ represents simple harmonic motion which takes the form
$y = 5 \sin (2 π t + \frac{π}{2})$
The equation
$y = 5 \cos (\frac{3 π}{2} - 2 π t)$ can be
Written as
$\begin{array}{l} y = 5 \cos (2 π t - \frac{3 π}{2}) (∵ \cos (- θ) = \cos θ) \\ \Rightarrow y = 5 \cos (\frac{π}{2} + 2 π t - 2 π) (∵ \frac{3 π}{2} = 2 π - \frac{π}{2}) \\ \Rightarrow y = 5 \cos (\frac{π}{2} + 2 π t) (∵ \cos (2 π - θ) = \cos θ) \\ y = - 5 \sin 2 π t (∵ \cos (\frac{π}{2} + θ) = - \sin θ) \end{array}$
Hence time period is 1 hour

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App