Question

The initial phase of a body executing SHM is $\dfrac{\pi }{4}$ then what will be its phase at the end of 10 oscillations?

Answer 1

Hint:A particle is said to be in simple harmonic motion if it moves back and forth around a fixed point under the influence of a restoring force that is directly proportional to the displacement from the fixed point and is always directed back to the fixed point. In basic harmonic motion, the initial phase is: The starting phase or epoch of a vibrating particle is defined as the phase of the particle at time \[t = 0.\].

Complete step by step answer:
When particles begin oscillation at a certain point, they will end up back at the same spot when the oscillation is completed. As a result, after completing 10 oscillations, all particles will be in the same place. So the final phase is $\dfrac{\pi }{4}$.

Additional Information:
Simple harmonic motion has the following properties: -
1. It can be represented in sine and cosine.
2. The particle's entire energy is conserved when it performs simple harmonic motion.
Swing, pendulum, bungee, jumping, cradle, etc. are examples of simple harmonic motion.
3. Every oscillatory motion has a period, but not all periodic motions are oscillatory.
4. Oscillatory motion is a back-and-forth movement around a fixed point.
5. The angle formed by a point in a uniform circular motion whose projection is that simple harmonic motion, with the original point of motion at the centre of the circular motion, is the phase of that point in simple harmonic motion.

Note:At the equilibrium position, a particle executing simple harmonic motion will have the highest speed, whereas at the extreme locations, it will have the lowest speed. The reciprocal of the particle's frequency will be its period of motion.