Question

5 & 6 please?

Explain why the period for a mass/ideal spring system on a frictionless not depend on the amplitude of the motion? What is the difference between oscillatory motion and simple harmonic motion?

Answer 1

6. Oscillation

Oscillations are a type of periodic motion. An oscillation is usually defined as a repetitive variation over time. The oscillation can occur over a middle equilibrium point or between two states. A pendulum is a good example for an oscillatory motion. The oscillations are mostly sinusoidal. An alternating current is also a good example for oscillation. In the simple pendulum, the bob oscillates over the middle equilibrium point. In an alternating current, the electrons oscillate inside the closed circuit over an equilibrium point. There are three types of oscillations. The first type is the un-damped oscillations in which the internal energy of the oscillation remains a constant. The second type of oscillations is the damped oscillations. In the case of damped oscillations, the internal energy of the oscillation decreases over time. The third type is the forced oscillations. In forced oscillations, a force is applied on the pendulum in a periodic variation to the pendulum.

Simple Harmonic Motion

The simple harmonic motion is defined as a motion taking the form of a = – (ω²) x where “a” is the acceleration and “x” is the displacement from the equilibrium point. The term ω is a constant. A simple harmonic motion requires a restoring force. The restoring force can be a spring, gravitational force, magnetic force, or an electric force. A simple harmonic oscillation will not emit any energy. The total mechanical energy of the system is conserved. If the conservation does not apply, the system will be a damped harmonic system. There are many important applications of simple harmonic oscillations. A pendulum clock is one of the best simple harmonic systems available. It can be shown that the period of the oscillation does not depend on the mass of the pendulum. If external factors such as air resistance affect the motion, it will eventually dampen and will stop. A real life situation is always a damped oscillation. A perfect spring mass system is also a good example for the simple harmonic oscillation. The force created by the elasticity of the spring acts as the restoring force in this scenario. The simple harmonic motion can also be taken as the projection of a circular motion with a constant angular velocity. At the equilibrium point, the kinetic energy of the system becomes a maximum, and at the turning point, the potential energy becomes a maximum and the kinetic energy becomes zero.

• Simple harmonic motion is a special case of oscillations.

• A simple harmonic motion is possible only in theory, but oscillations are possible in any situation.

• The total energy of the simple harmonic motion is constant whereas the total energy of an oscillation, in general, needs not to be constant.