# Quiz 13: Vibrations and Waves

(a) The expression for the total energy of the particle executing Simple harmonic motion is, Here, m is the mass of the particle, is the angular frequency of oscillation, and is the amplitude of the particle. From the above expression, keeping the other parameters constant, it is clear that the total energy of the particle in the simple harmonic motion is directly proportional to the square of the amplitude of the particle. Therefore, if the amplitude of a particle in the simple harmonic motion is doubled, then the total energy of the particle will be four times its initial energy. (b) The expression for the maximum speed of the particle in simple harmonic motion is, Since, the maximum speed of the particle is directly proportional to the amplitude of the particle. Therefore, if the amplitude of the particle is doubled then the speed of the particle will also be doubled.

The amplitude of a particle is the maximum displacement produced by that particle in a simple harmonic motion. For one period, the particle travels a distance which is equal to 4 times its amplitude. Calculate the distance of the particle in 3 periods as follows: Thus, the particle travels in 3 periods is .

In simple harmonic motion, the particle moves again and again over the same path about a fixed point (equilibrium position). SHM is defined as the motion of an oscillatory particle which is acted upon by a restoring force , which is directly proportional to the displacement and opposite in direction. Hence, the correct answer is option .