0.28 kg mass is attached to a light spring with a force constant of 30.9 N/m and set into oscillation on a horizontal frictionless surface. If the spring is stretched 5.0 cm and leased from rest, determine the following. (a) maximum speed of the oscillating mass 525 m/s (b) speed of the oscillating mass when the spring is compressed 1.5 cm .53 X Is energy conserved for this oscillating system? m/s (c) speed of the oscillating mass as it passes the point 1.5 cm from the equilibrium position .53 X When the mass-spring system is oscillating, how does the speed of the oscillating mass when the spring is compressed a certain amount compare to when it is stretched the same amount? m/s (d) value of x at which the speed of the oscillating mass is equal to one-half the maximum value 177 X Is energy conserved for this oscillating system? m Additional Materials Reading
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
Given
Mass m = 0.28 kg
Force constant k = 30.9 N/m
Amplitude ( max displacement )
a = 5 cm = 0.05 m
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