One end of a light spring with spring constant k, is attached to the ceiling. A second light spring is attached to the lower end, with spring constant k,. An object of mass m is attached to the lower end of the second spring. (a) By how much does the pair of springs stretch? (Use the following as necessary: k,, k,, m, and g, the gravitational acceleration.) Xtotal = (b) What is the effective spring constant of the spring system? (Use the following as necessary: k,, ka, m, and g, the gravitational acceleration.) keff = (c) What If? Two identical light springs with spring constant k, are now individually hung vertically from the ceiling and attached at each end of a symmetric object, such as a rectangular block with uniform mass density. In this case, with the springs next to each other, we describe them as being in parallel. Find the effective spring constant of the pair of springs as a system in this situation in terms of kz. (Use the following as necessary: ka, M, the mass of the symmetric object, and g, the gravitational acceleration.) keff =
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.
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