A 0.26 kg mass is attached to a light spring with a force constant of 36.9 N/m a

Question

A 0.26 kg mass is attached to a light spring with a force constant of 36.9 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

Mass of the object, m = 0.53 kg

Force constant, k = 23.2 N/m

Angular frequency, ? = ? (k/m) = 11.91 rad/s

                                 = 6.62 rad/s

Solution:

(a)

Amplitude, A = 0.05 m

Maximum speed, vmax = ? A

                                    = 11.91* 0.05

                                    = 0.596m/s

(b)

Distance of compression, x = 0.015 m

Speed, v = ? ? [A^2 - x^2]

              = 11.91 ? [0.05^2 - 0.015^2]

              = 0.568 m/s

(c)

Distance of stretching, x = 0.015 m

Speed, v = ? ? [A^2 - x^2]

              = 11.91 ? [0.05^2 - 0.015^2]

              = 0.568 m/s

(d)

v = vmax / 2

? ? [A^2 - x^2 ] = ? A / 2

A^2 - x^2 = A^2 / 4

x^2 = 3 A^2 / 4

x = (?3 / 2) A

   = 0.866 * 0.05

   = 0.0433 m

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