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Physicists often take a complex problem and reduce it to a simpler, more manageable problem. This is simpler because we know that the spring obeys Hooke’s law, so that force is proportional to displacement.

The equation a = −ω2x which describes s.h.m. can be solved to give the sine and cosine equations we have considered above.

Once physicists have solved one problem like this, they look around for other situations where they can use the same
ideas all over again. So the mass–spring theory also works well for vibrating atoms and molecules, for objects bobbing up and down in water, and in many other situations.

Physicists also seek to modify the theory to fit a greater
range of situations. For example, what happens if the
vibrating mass experiences a frictional force as it oscillates?
(This is damping, as discussed above.)

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Displacement-distance of the object from an equilibrium point
Amplitude- maximum displacement of an oscillating object
Period-time taken for a single oscillation
Frequency-number of oscillation per second

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A signal  generator set to low frequency  drives a loudspeaker cone so that it vibrates.
Use a stroboscope flashing at similar frequency to show up the movement of the cone

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A trolley loaded with extra masses is tethered by identical springs in between two clamps.
Displace the trolley to one side and it will oscillate back and forth

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- if natural frequency of oscillation is equal to forced frequency, damping decreases causing destruction of an object
- achieved by introducing force of friction into the mechanical system
- for example: destruction af a building

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Derivation Of Equation Of Frequency And Period S.H.M

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Derivation Of Equation Of Frequency And Period S.H.M

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-Resonance can increase the amplitude of an oscillation by applying force at just the right frequency

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When a body oscillates by being influenced by an external periodic force, it is called forced oscillation. Here, the amplitude of oscillation, experiences damping but remains constant due to the external energy supplied to the system.For example, when you push someone on a swing, you have to keep periodically pushing them so that the swing doesn’t reduce.

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The free oscillation possesses constant amplitude and period without any external force to set the oscillation. Ideally, free oscillation does not undergo damping. But in all natural systems damping is observed unless and until any constant external force is supplied to overcome damping. In such a system, the amplitude, frequency, and energy all remain constant.

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constant interchange energy between two forms

potential energy - maximum at both ends  of amplitude

kinetic energy - at equilibrium, kinetic energy is maximum

total energy remains constant throughout : k.e + p.e has the same value

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If an oscillator is displaced and then released it will begin to vibrate. If no more external forces are applied to the system it is a free oscillator. If a force is continually or repeatedly applied to keep the oscillation going, it is a forced oscillator.

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a = -ω²r

a ∝ x

minus sign shows that when object displaced to right, direction of acceleration is to the left

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The frequency of s.h.m is equal to the number of oscillations per unit time

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1. Light damping: system oscillates about equilibrium position with decreasing amplitude over a period of time

2. Critical damping: system does not oscillate & is amount of damping required such that the system returns to its equilibrium position in the shortest possible time

3. Heavy damping: damping is so great that the displaced object never oscillates but returns to its equilibrium
position very very slowly

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Damping: loss of energy and reduction in amplitude from an oscillating system caused by force acting in opposite direction to the motion (e.g. friction)

Resonance: the maximum amplitude of vibration when impressed frequency equals natural frequency of vibration

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Vibration / oscillation in which there is acceleration towards a fixed point. The magnitude of the acceleration is proportional to the displacement from the point.

Requirement s.h.m

1. the mass that oscillates

2. a position where the mass is in equilibrium

3. a restoring force that acts to return the mass to equilibrium position