A mass is connected to a horizontal spring. If a force of 13 N is applied to the spring, it stretches by 17.5 cm. (a) If you compress the spring 22.5 cm from the equilibrium position, how much potential energy (in J) does it have? (b) If you then release the spring so that the mass is now 9.5 cm from the equilibrium position, how much potential energy (in J) does it have now? (c) What is the change in potential energy (in J) from part (a) to part (b)?
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.
A mass is connected to a horizontal spring. If a force of 13 N is applied to the spring, it stretches by 17.5 cm.
(a) If you compress the spring 22.5 cm from the equilibrium position, how much potential energy (in J) does it have?
(b) If you then release the spring so that the mass is now 9.5 cm from the equilibrium position, how much potential energy (in J) does it have now?
(c) What is the change in potential energy (in J) from part (a) to part (b)?
(d) How much work (in J) did the spring do on the mass when the mass is moved from its position in part (a) to its position in part (b)?
(e) How much work (in J) did you do on the mass to allow the spring to move from its position in part (a) to its position in part (b)?
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