PDF The Will’s Harmonic Motion

Lab 7 - Simple Harmonic Motion

Account Options Sign in. My library Help Advanced Book Search. Get print book. Fadel Sabry. Are human beings born with a moral character, or does our character form and change as we experience life? Selected pages Title Page. Table of Contents. Contents Part II. In addition, other phenomena can be approximated by simple harmonic motion, including the motion of a simple pendulum as well as molecular vibration.

Simple Harmonic Motion – Concepts

Simple harmonic motion is typified by the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's law. The motion is sinusoidal in time and demonstrates a single resonant frequency. For simple harmonic motion to be an accurate model for a pendulum, the net force on the object at the end of the pendulum must be proportional to the displacement. This is a good approximation when the angle of the swing is small.

Simple harmonic motion provides a basis for the characterization of more complicated motions through the techniques of Fourier analysis. The motion of a particle moving along a straight line with an acceleration whose direction is always towards a fixed point on the line and whose magnitude is proportional to the distance from the fixed point is called simple harmonic motion [SHM].

In the diagram, a simple harmonic oscillator , consisting of a weight attached to one end of a spring, is shown.

CALCULUS - Simple Harmonic Motion

The other end of the spring is connected to a rigid support such as a wall. If the system is left at rest at the equilibrium position then there is no net force acting on the mass. However, if the mass is displaced from the equilibrium position, the spring exerts a restoring elastic force that obeys Hooke's law. Once the mass is displaced from its equilibrium position, it experiences a net restoring force. As a result, it accelerates and starts going back to the equilibrium position.

When the mass moves closer to the equilibrium position, the restoring force decreases. At the equilibrium position, the net restoring force vanishes. Therefore, the mass continues past the equilibrium position, compressing the spring. The motion is sinusoidal in time and demonstrates a single resonant frequency.

For simple harmonic motion to be an accurate model for a pendulum, the net force on the object at the end of the pendulum must be proportional to the displacement. This is a good approximation when the angle of the swing is small.

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Simple harmonic motion provides a basis for the characterization of more complicated motions through the techniques of Fourier analysis. The motion of a particle moving along a straight line with an acceleration whose direction is always towards a fixed point on the line and whose magnitude is proportional to the distance from the fixed point is called simple harmonic motion [SHM].

Lab 7 - Simple Harmonic Motion

In the diagram, a simple harmonic oscillator , consisting of a weight attached to one end of a spring, is shown. The other end of the spring is connected to a rigid support such as a wall. If the system is left at rest at the equilibrium position then there is no net force acting on the mass. However, if the mass is displaced from the equilibrium position, the spring exerts a restoring elastic force that obeys Hooke's law.

15.1 Simple Harmonic Motion

Once the mass is displaced from its equilibrium position, it experiences a net restoring force. As a result, it accelerates and starts going back to the equilibrium position. When the mass moves closer to the equilibrium position, the restoring force decreases. At the equilibrium position, the net restoring force vanishes. Therefore, the mass continues past the equilibrium position, compressing the spring. A net restoring force then slows it down until its velocity reaches zero, whereupon it is accelerated back to the equilibrium position again.

As long as the system has no energy loss, the mass continues to oscillate.

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