If the equation of motion of a particle is given by s = a cos(ωt + δ), the particle is said to undergo simple harmonic motion. (a) find the velocity of the particle at time t. s'(t) = −aωsin(ωt+δ) correct: your answer is correct. (b) when is the velocity 0? (use n as the arbitrary integer.)

The periodic motion of the particle consists of velocities that are within a

given range and a domain that extends to infinity.

Reasons:

The given parameters are;

The function for the motion of the particle is; s = a·cos(ω·t + δ)

The velocity of the particle is found as s'(t) = -a·ω·sin(ω·t + δ)

Required:

The time at which the velocity is zero

Solution:

At zero velocity, we have;

The input variable is the time, t, therefore;

sin(ω·t + δ) = 0

From the attached graph, the value of sin(θ) is zero for multiples of π,

therefore, we have;

sin(ω·t + δ) = sin(n·π), where; n is an integer

Which gives;

Making t subject of the above formula gives;

Therefore;

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Simple harmonic motion

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You need to solve

for . If , then we must have

We have for , where is any integer, so