Important Terms In Simple Harmonic Motion - Practice Questions & MCQ

1. Amplitude:- 

We know that displacement of a particle in SHM is given by:

The quantity A is called the amplitude of the motion. It is a positive constant which represents the magnitude of the maximum displacement of the particle from mean position in either direction.

2. Time period:-

• In SHM, a particle repeats its motion after a fixed interval of time. And this time interval after which the particle repeats its motion is called time period. It is denoted by T.
• Time period is also defined as the time taken to complete one oscillation. And after one time period, both displacement and velocity of the particle are repeated.
• We know that:-

If a motion is periodic with a period T, then the displacement x (t) must return to its initial value after one period of the motion; that is, x (t) must be equal to x (t + T ) for all t and velocity v(t) must also return to its initial value, i.e., v(t) must be equal to v(t+T). So,

And

As we know both Sine and Cosine function repeats itself when their argument increases by 2π,i.e.,

• Time period can also be written as:-

3. Frequency:-

The reciprocal of T gives the number of repetitions that occur per unit time. This quantity is called the frequency of the periodic motion.

• It is denoted by f.

• The unit of frequency is or Hertz(Hz).

4. Phase:-

• 
• It determines the status of the particle in simple harmonic motion.
• If the phase is zero at a certain instant, then:

which means that the particle is crossing the mean position and is going towards the positive direction. 

             Fig:- Status of the particle at different phases

5. Phase constant:-

• The constant   is called the phase constant (or phase angle). 

• The value of  depends on the displacement and velocity of the particle at t = 0 or we can say the phase constant signifies the initial conditions.

• Any instant can be chosen as t = 0 and hence the phase constant can be chosen arbitrarily.