A 1kg-block oscillates on a spring with spring constant 20 N/m on a frictionless surface. At t = 0 s the block is 20 cm to the right from the equilibrium position, moving to the left with a speed of 100 cm/s. Determine: (1) Sketch/model the situation indicating the positive direction and the initial conditions. (2) Calculate the period of the oscillation. (3) Calculate the total energy of the system. (4) Calculate the amplitude. (5) Calculate the phase angle. (6) Calculate the maximum velocity. (7) Calculate the maximum acceleration.
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 1kg-block oscillates on a spring with spring constant 20 N/m on a frictionless surface. At t = 0 s the block is 20 cm to the right from the equilibrium position, moving to the left with a speed of 100 cm/s. Determine:
(1) Sketch/model the situation indicating the positive direction and the initial conditions.
(2) Calculate the period of the oscillation.
(3) Calculate the total energy of the system.
(4) Calculate the amplitude.
(5) Calculate the phase angle.
(6) Calculate the maximum velocity.
(7) Calculate the maximum acceleration.
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