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Harmonic vibration of a mass

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A mass of 0.3 kg is suspended from a spring of stiffness 200 N m-1. If
the mass is displaced by 10 mm from its equilibrium position and
released, for the resulting vibration, calculate:
(a) (i) the frequency of vibration.
(ii) the maximum velocity of the mass during the vibration.
(iii) the maximum acceleration of the mass during the vibration.
(iv) the mass required to produce double the maximum velocity.
calculated in (ii) using the same spring and initial deflection.
(b) Plot a graph of acceleration against displacement (x) (for values of x
from x = -10 mm to x = +10 mm).

Solution Summary

A numerical application of a harmonic vibration of a mass attached to a spring is solved, finding the maximum velocity and acceleration.

Solution Preview

A mass of 0.3 kg is suspended from a spring of stiffness 200 N m-1. If the mass is displaced by 10 mm from its equilibrium position and released, for the resulting vibration, calculate:
(a) (i) the frequency of vibration.
(ii) the maximum velocity of the mass during the vibration.
(iii) the maximum acceleration of the mass during the vibration.
(iv) the mass required to produce double the maximum velocity calculated in (ii) using the same spring and initial deflection.
(b) Plot a graph of acceleration against displacement (x) (for values of x
from x = -10 mm to x = +10 mm).

Solution:

(a) (i) The frequency of vibration is given by the formula
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