A 0.13 kg block oscillates back and forth along a straight line on a frictionles

Question

A 0.13 kg block oscillates back and forth along a straight line on a frictionless horizontal surface. Its displacement from the origin is given by x = (15 cm)cos[(8 rad/s)t + /2 rad)]. (a) What is the oscillation frequency? Hz (b) What is the maximum speed acquired by the block? cm/s At what value of x does this occur? cm (c) What is the maximum acceleration of the block? cm/s2 At what values of x does this occur? (positive then negative) cm and cm (d) What force, applied to the block, results in the given oscillation? ( N/m)x

Explanation / Answer

(a)

f = w/ 2pi = 8/ 2pi = 1.27 Hz

(b)

vmax = A w = 15 cm( 8 rad/s) = 120 cm/s

x = 0

(c)

a = - w^2 A = -(8)^2 ( 15 cm) =- 960 cm/s^2

since w = - w^2 x

when x = A , a = a_max

so maxiunun occurs

x= + 15 cm and -15 cm

(d)

F = -kx = - mw^2 x

= -(0.13)( 8)^2 x

=(-8.32 N/m)x

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