Simple harmonic oscillators can be used to model many different types of systems. Consider a block of mass (m = 2 kg), originally at rest, that slides down a frictionless ramp which makes an angle (θ= 30degrees) with the horizontal. At the bottom of the ramp, the block rebounds (without losing energy)and slides back up the ramp. When the block gets to its original position, it begins to slide back down the block. At the starting point, let the block be at a height (H = 4 m). (a) Let h(t) be the block’s height as a function of time. What is the amplitude of the block’s oscillations? (b) What is the period (T) of the block’s oscillations?
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.
Simple harmonic oscillators can be used to model many different types of systems. Consider a block of mass (m = 2 kg), originally at rest, that slides down a frictionless ramp which makes an angle (θ= 30degrees) with the horizontal. At the bottom of the ramp, the block rebounds (without losing energy)and slides back up the ramp. When the block gets to its original position, it begins to slide back down the block. At the starting point, let the block be at a height (H = 4 m). (a) Let h(t) be the block’s height as a function of time. What is the amplitude of the block’s oscillations? (b) What is the period (T) of the block’s oscillations?
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