A 0.580-kg object attached to a spring with a force constant of 8.00 N/m vibrate

Question

A 0.580-kg object attached to a spring with a force constant of 8.00 N/m vibrates in simple harmonic motion with an amplitude of 10.4cm.

(a) Calculate the maximum value of its speed.
_______________ cm/s

(b) Calculate the maximum value of its acceleration.
_______________ cm/s2

(c) Calculate the value of its speed when the object is 6.40 cm from the equilibrium position.
_______________ cm/s

(d) Calculate the value of its acceleration when the object is 6.40 cm from the equilibrium position.
________________ cm/s2

(e) Calculate the time interval required for the object to move from x = 0 to x = 2.40 cm.
_________________ s

Explanation / Answer

Consider x(t) = Asin(?t - ?), and we can take ? = 0 here.
Then velocity,

dx(t)/dt = v(t) = A?cos(?t)
and acceleration,

d2x/dt2 = a(t) = -A?

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