An object attached to a spring vibrates with simple harmonic motion as described

Question

An object attached to a spring vibrates with simple harmonic motion as described by the figure below.

(a) For this motion, find the amplitude.
___________cm

(b) For this motion, find the period.
___________s

(c) For this motion, find the angular frequency.
___________rad/s

(d) For this motion, find the maximum speed.
___________cm/s

(e) For this motion, find the maximum acceleration.
___________cm/s2

(f) For this motion, find an equation for its position x in terms of a sine function.

______________________

Explanation / Answer

part a )

amplitude = max acceleration = 2 cm

part b )

compeleting one cycle = 4s

part c )

w = 2pi/T

w = pi/2 = 1.57 rad/s

part d )

max speed

aw = 2 * pi/2 = pi = 3.14 cm/s

part e )

max acceleration

aw^2 = 2 * pi^2/4 = 4.93 cm/s^2

part f )

y = Asin(wt + phi)

y = 2 sin(pi *t/2 )

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