A 0.87 kg block oscillates back and forth along a straight line on a frictionles

Question

A 0.87 kg block oscillates back and forth along a straight line on a frictionless horizontal surface. Its displacement from the origin is given by
x = (11 cm)cos[(16 rad/s)t + /2 rad]
(a) What is the oscillation frequency? (b) What is the maximum speed acquired by the block? (c) At what value of xdoes this occur? (d) What is the magnitude of the maximum acceleration of the block? (e) At what positive value of xdoes this occur? (f) What force, applied to the block by the spring, results in the given oscillation?

Explanation / Answer

Here ,

as x = A * cos(w * t + phi)

x = (11 cm)cos[(16 rad/s)t + /2 rad]

comparing equations

a) w = 16 rad/s

oscillation frequency = w/(2pi)

oscillation frequency = 16/(2pi)

oscillation frequency = 2.55 rad/s

b) maximum speed = A * w

maximum speed = 0.11 * 16 m/s

maximum speed = 1.76 m/s

c)

maximum speed occurs at the equilibrium

x = 0 cm.

d)

magnitude of maximum acceleration = A * w^2

magnitude of maximum acceleration = 0.11 * 16^2

magnitude of maximum acceleration = 29.7 m/s^2

e)

the acceleration is maximum at the extremes

hence, at x = 11 cm , - 11 cm

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