Question:

If x,vx, v and aa denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period TT, then, which of the following does not change with time?

Updated On: Jul 28, 2022
  • a2T2+4π2v2a^2 T^2 +4 \pi^2 v^2
  • aTx\frac{a T}{x}
  • aT+2πvaT + 2 \pi v
  • aTv\frac{a T}{v}
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The Correct Option is B

Solution and Explanation

For a particle executing simple harmonic motion, acceleration, a=ω2xa = - \omega^2 x where ω=2πT\omega = \frac{2 \pi}{T} a=4π2T2x a = - \frac{4 \pi^2}{T^2} x or aTx=4π2T\frac{aT}{x} = - \frac{4 \pi^2}{T} The period of oscillation T is a constant.   aTx \therefore \:\: \frac{aT}{x} is a constant.
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Concepts Used:

Acceleration

In the real world, everything is always in motion. Objects move at a variable or a constant speed. When someone steps on the accelerator or applies brakes on a car, the speed of the car increases or decreases and the direction of the car changes. In physics, these changes in velocity or directional magnitude of a moving object are represented by acceleration

acceleration