First slide

Simple hormonic motion

Question

Find the distance covered by a particle from time t = 0 to t = 6 sec, when the particle follows the movement according to $y = a \cos (\frac{π}{4}) t$ ,

Difficult

A

a
B

2a
C

3a
D

4a

Solution

Comparing with y = a cos $ωt$
$ω = \frac{π}{4} = \frac{2 π}{T}$ will give T = 8 seconds
y = a at t = 0
So, particle is at extreme position at t= 0. Its time period is 8 seconds.
So, in time t = 0 to t = 6 seconds, it will be at the mean position. So, distance covered = 3a..

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