A 3 kg object is attached to a spring and released into SHM. If the spring oscil

Question

A 3 kg object is attached to a spring and released into SHM. If the spring oscillates with a frequency of 2 Hz and has an amplitude of 16 cm, what are the position, velocity, and acceleration after 2.52 seconds?

Position =  [Num]meters

Velocity = [Num]m/s

Acceleration = [Num]m/s2

A 3 kg object is attached to a spring and released into SHM. If the spring oscillates with a frequency of 2 Hz and has an amplitude of 16 cm, what are the position, velocity, and acceleration after 2.52 seconds?

Position =  [Num]meters

Velocity = [Num]m/s

Acceleration = [Num]m/s2

Explanation / Answer

Here ,

as the position of the particle is given as

x = A * sin(2pi*f * t)

x = 0.16 * sin(2pi * 2 * t)

x = 0.16 * sin(12.56 * t)

NOw , as t = 2.52 s

x = 0.16 * sin(12.56 * 2.52)

x = 0.0372 m

the postion is 0.0372 m

Now ,
velocity = x * 2pi * f

velocity = 0.0372 * 12.56

velocity = 0.467 m/s

Now , for acceleration of

a = v * 2pi *f

a = - 0.467 * 12.56 m/s^2

a = - 5.87 m/s^2

the acceleration is -5.87 m/s^2

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