A particle is undergoing simple harmonic motion with a period of

SOLUTION

CONCEPT:

• Wave: It is a disturbance that transfers energy from one place to another.
• SHM (Simple harmonic motion): The type of oscillatory motion in which the restoring force on the system is directly proportional to the displacement of the system is called SHM.

The general expression for the simple harmonic equation is given by:

X = A Sin (ω t)

Where A is the amplitude of SHM, ω is the angular frequency and t is time

The velocity (V) of a particle at any position is given by:

\(V = ω \sqrt {{A^2} - {x^2}}\)

The relation between Time period (T) and angular frequency (ω) is given by:

T = 2π/ω 

CALCULATION:

Given that:

Time period (T) = 2 sec

Amplitude (A) = 2 m

Angular frequency (ω) = 2π/T = 2π/2 = π rad/s

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Since \(V = ω \sqrt {{A^2} - {x^2}}\)

• The speed or velocity (V) of the particle will be maximum at the mean position (x = 0).

\(Maximum\;velocity\;\left( V \right) = ω \;\sqrt {{A^2} - {x^2}\;} = ω \;\sqrt {{A^2} - {0^2}} = ω \;A = π \times 2\;m/s \)

So maximum speed (V) = 2π m/s

Hence option 2 is correct.