Question

The displacement of a particle executing simple harmonic motion is given by x = 2cos(t) where t is the time in seconds then the time period of the particle is:

• A. π second
• B. 2π second
• C. 3π second
• D. 0.5π second

Answer 1

Answer: (B)

2π second

Answer 2

The correct option is: (B) 2π second.

The equation for simple harmonic motion (SHM) is given by:

x = A cos(ωt)

Where:

• x is the displacement of the particle from its equilibrium position.
• A is the amplitude of the motion.
• ω is the angular frequency (in radians per second).
• t is the time in seconds.

In the provided equation, x = 2cos(t), we can see that the amplitude is 2.

For simple harmonic motion, the relation between the angular frequency (ω) and the time period (T) is:

ω = 2π / T

Given that ω = 1 (since the coefficient of 't' in the equation is 1), we can rearrange the relation to solve for the time period:

T = 2π / ω

Substituting the value of ω = 1:

T = 2π / 1 = 2π seconds.