You build a t-shirt launcher for basketball games using a compressible spring. The mass of the t-shirt is 0.2 kg. The spring has a stiffness 390 N/m, and its unstretched length is 0.6 m. To launch a t-shirt, you hold a shirt in your hand, use it to push it down on the spring until the spring's length is 0.2 m, and then you latch the spring to hold it at rest before the launch. A picture of the spring and t-shirt is shown below. Figure A shows the spring when it is relaxed. Figure B shows the partially compressed spring as you are pushing it downward, and Figure C shows the spring when it is fully compressed. (The picture is not drawn to scale.) You can assume you push it downward at constant speed. Lo=0.6 m W = A m W = B m HOODO C (a) How much work did you do on the spring in order to compress the spring? L=0.2 m (b) To launch a second t-shirt, you repeat the procedure but this time you compress the spring only half as much (so its compressed length is 0.4 m). In this case, how much work did you do on the spring in order to compress the spring?

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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.