A 0.39 kg block oscillates back and forth along a straight line on a frictionles

Question

A 0.39 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 = (7 cm)cos[(12 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 magnitude of the maximum acceleration of the block? cm/s2 At what values of x does this occur? (Type your answers in any order. If there is only one answer, type 'none' in the second box.) 1= cm 2= cm (d) What force, applied to the block, results in the given oscillation? (N/cm)x

Explanation / Answer

The 0.39 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 = (13 cm)cos[(5 rad/s) t + ? /2 rad)] (a) What is the oscillation frequency? 1 Hz (b) What is the maximum speed acquired by the block? 2 cm/s At what value of x does this occur? 3 cm (c) What is the maximum acceleration of the block? 4 cm/s 2 At what values of x does this occur? (positive then negative) 5 cm and 6 cm

x = (13 cm)cos[(5 rad/s)t + p/2 rad)]

x=Acos(t+)=5 A=13cm

a)oscillation frequency=f=2=10b)x'=-Asin(t+)maximum speed acquired by the block=x'|max=-A=65cm/sat X=0 equillibrium positionc)x"=-2Acos(t+)x"|max=-2A=-325cm/s2cos(t+)=1=cos0 or cos2t+=0 or 2x=A=13cmd)F=ma=0.39x325cm/s2=1.2675N

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