A child rolls a marble on a bent track that is 100 cm long. We use x to represent the position of the marble along the track. On the horizontal sections from x=0 to x=20cm and from x=40cm to x=60cm, the marble rolls with constant speed. On the sloping sections, the marbles speed changes steadily. At the places where the slope changes, the marble stays on the track and does not undergo any sudden changes in speed. The child gives the marble some initial speed at x=0 and t=0 and then watches it roll to x=90cm, where it turns around, eventually returning to x=0 with the same speed with which the child released it. Prepare graphs of x versus t, vxversus t, and ax versus t, vertically aligned with their time axes identical, to show the motion of the marble. You will not be able to place numbers other than zero on the horizontal axis or on the velocity or acceleration axes, but show the correct graph shapes.
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 child rolls a marble on a bent track that is 100 cm long. We use x to represent the position of the marble along the track. On the horizontal sections from x=0 to x=20cm and from x=40cm to x=60cm, the marble rolls with constant speed. On the sloping sections, the marbles speed changes steadily. At the places where the slope changes, the marble stays on the track and does not undergo any sudden changes in speed. The child gives the marble some initial speed at x=0 and t=0 and then watches it roll to x=90cm, where it turns around, eventually returning to x=0 with the same speed with which the child released it. Prepare graphs of x versus t, vxversus t, and ax versus t, vertically aligned with their time axes identical, to show the motion of the marble. You will not be able to place numbers other than zero on the horizontal axis or on the velocity or acceleration axes, but show the correct graph shapes.
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