Question

A device is designed in such a way that it displays green light whenever its speed is increasing and a blue light when the speed is decreasing. If the device is performing SHM with a time period of 12s and it starts from the extreme position, when is the device green?

• A. at t = 1 seconds
• B. at t = 3.2 seconds
• C. at t = 7 seconds
• D. at t = 11 seconds

Answer 1

Answer: (A), (C)

The correct options are
A

at t = 1 seconds

C

at t = 7 seconds

When the body is at any of the extremes the restoring force either pulls it or pushes it towards the mean position. i.e., the body accelerates.

T-time period=12

$\Rightarrow t_{AO}+t_{OB}+t_{BO}+t_{OA}=T=12$

$t_{AO}=t_{OB}=t_{BO}=t_{OA}=3sec$

let's say

particle starts from extreme position A

so for first 3 sec particle accelerates

hence option A is correct

After crossing mean position the spring has stretched now and will try to pull block back. So block decelerates. So from (t = 3 to t = 6) body decelerates. Hence blue light so option B is wrong.

Again B to O ,particle coming from extreme. Spring is stretched, so will pull the body towards mean position. Velocity and force in same direction. so acceleration. (t = 6 to t = 9) body accelerates, green light.option (c) correct

After particle crosses mean i.e., O to A, spring is compressed, pushes towards mean position. Velocity is towards A but acceleration(force) towards O, Opposite direction , so deceleration. Blue light.

(t = 9 to t = 12)

So option D is wrong.