Question

A simple pendulum performs simple harmonic motion with an amplitude of 0.7 m and frequency ω. The speed of pendulum at a time t is expressed as:
1. 1.4cos²ωt
2. 0.7ωsin²ωt
3. 0.7ωcosωt
4. 1.4cosωt

Answer 1

Correct Answer - Option 3 : 0.7ωcosωt

The correct answer is option 3) i.e. 0.7ωcosωt

CONCEPT:

• Simple harmonic motion(SHM): It is a type of oscillatory motion in which the restoring force is directly proportional to the displacement of the body from its mean position.
  • ​This means that the net force which in turn is the acceleration is proportional to the displacement of the object and acts in the opposite direction of the displacement.
  • The displacement in an SHM for a system starting at equilibrium(x = 0) is given by the equation:

 \(x = asinω t\)

​​​Where x is the displacement, a is the amplitude, ω is the angular frequency and t is the time taken. 

EXPLANATION:

The displacement of the given pendulum is \(x = asinω t\)

Speed, v \(=\frac{dx}{dt} =\frac{d(asin ω t)}{dt} =a ω cosω t \)

Given that amplitude = 0.7 m,

⇒ Speed, v = 0.7ωcosωt