A 0.38 kg mass is attached to a light spring with a force constant of 21.9 N/m a

Question

A 0.38 kg mass is attached to a light spring with a force constant of 21.9 N/m and set into oscillation on a horizontal frictionless surface. If the spring is stretched 5.0 cm and released from rest, determine the following.

(a) maximum speed of the oscillating mass (m/s)

(b) speed of the oscillating mass when the spring is compressed 1.5 cm (m/s)

(c) speed of the oscillating mass as it passes the point 1.5 cm from the equilibrium position (m/s)

(d) value of x at which the speed of the oscillating mass is equal to one-half the maximum value (m)

Explanation / Answer

(a)since energy will be conserved,velocity will be max. when potential energy is 0

1/2kx^2=1/2mv^2;

v^2 =(21.9*0.05^2)/0.38

v=0.38 m/s

(b) conserving energy:

1/2kx^2=1/2mv^2 + 1/2kx'^2

v^2=(21.9(0.05^2 - 0.015^2))/0.38

v=0.13 m/s

(c) v=0.13 m/s on both sides of equilibrium as equation will remain same as above

(d) conserving energy:

1/2kx^2=1/2mv^2 + 1/2kx''^2

here v=1/2 v max; v=0.38/2=0.19 m/s

x''=4.33 cm

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