Ncert Exercises & Solutions

The following statements are given for a simple harmonic oscillator.

a.	Force acting is directly proportional to the displacement from the mean position and opposite to it.
b.	Motion is periodic.
c.	Acceleration of the oscillator is constant.
d.	The velocity is periodic.

Choose the correct alternatives:

1. (a, b, d)

2. (a, c)

3. (b, d)

4. (c, d)

(1) Hint: Apply the concept of SHM.

Step 1: Find the velocity.

Let the equation for the SHM is, x=a sin

ω t

Clearly, it is a periodic motion because it involves sine function.

Velocity v

= \frac{d x}{d t} = \frac{d}{d t}

(asin

ω t

)=a

ω

cos

ω t

Velocity is also periodic because of the cosine function.

Step 2: Find the acceleration.

Acceleration,

A = \frac{d v}{d t} = \frac{d^{2} x}{d t^{2}} = - a ω^{2} \sin ω t

[

∵

Acceleration is a sine function, hence cannot be constant]

= - (ω^{2} a) \sin ω t = - ω^{2} x

Step 3: Find the force.

Force, F=mass x acceleration

=mA=-

m ω^{2} x

Hence, the force acting is directly proportional to the displacement from the mean position and opposite to it.