draw the displacement time graph for simple hormonic motion
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Displacement-time graphs show how the displacement of a moving object changes with time. In a displacement-time graph, the slope or gradient of the line, is equal to the velocity of the object. The steeper the line (and the greater the gradient) the faster the object is moving.
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For the SHM,
The displacement of the particle is given by, x=Acosωt
Velocity, v=
dt
dx
=
dt
d
(Acosωt)=−Aωsinωt
Acceleration, a=
dt
dv
=
dt
d
(−ωAsinωt)=−ω
2
Acosωt.
The corresponding velocity-time and acceleration time graph is as shown in the figure.
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