A 0.15 kg block oscillates back and forth along a straight line on a frictionles

Question

A 0.15 kg block oscillates back and forth along a straight line on a frictionless horizontal surface. Its displacement from the origin is given by the following equation. x = (8 cm)cos[(10 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 ofxdoes this occur?
cm

(c) What is the magnitude of the maximum acceleration of the block?
cm/s2
At what values ofxdoes this occur? (Type your answers in any order. If there is only one answer, type 'none' in the second box.)
cm
cm

Explanation / Answer

(a) f = 10/(2*pi) =1.59 Hz (b) s(max) = 8*10 cm/s = 80 cm/s = 0.8 m/s (c) x = 0 cm (d) a(max) = 8*10*10 cm/s/s = 800 cm/s/s = 8 m/s/s (e) x = 8 cm (f) f = m*a = 0.15 * 8 * sin[(10 rad/s)t] kg*m/s/s = 1.2 *sin[(10rad/s)t] Newtons

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