We know that oscillations are the motions which repeat themselves again and again. Simple harmonic motion is also type of oscillations which can be written as equation in form of sine or cosine form. They are also called periodic motions because it repeats after certain period. Particles of wave also follow periodic motion. So the equation of SHM resembles with wave equation almost.
There are various parameters of SHM like period, amplitude, phase etc. that needs to understand clearly. Phase depend on initial position of particle. For better understanding of SHM, we visualize particle doing uniform circular motion. We can solve problems this way easily with some caution about phase and other things in circular motion. We can know about velocity and acceleration of particle by differentiating equation of motion. Then learn about force law which causes this motion.
From force law equation we can get angular frequency. Total energy of SHM remains constant but KE and PE inter-converts constantly. Two SHMs can be superimposed to produce another one, but it’s not necessary that resultant motion will be always periodic. This is similar to superposition of waves.
There some examples of SHM in everyday life like oscillation due to spring and simple pendulum. Have a look on their equations and parameters. In real, particle doesn’t do ideal oscillations but it does damped oscillations. Here damping occurs due to resistive force of surrounding medium which is dependent of velocity of particle at that moment. Due to this, amplitude decreases exponentially.
It’s good to know equations of this. Unless external force is applied on oscillating system, it’ll oscillate with natural frequency, otherwise it’ll be forced oscillations. When this external force is equal to natural frequency, resonance will occur. At resonance frequency, system will oscillate at maximum amplitude.
Mistakes/challenges-
- First you should be able to recognize whether given equation is of SHM/periodic motion or not. For that conditions should be satisfied.
- Solving SHM problem with circular motion, don’t mistake in considering initial phase of particle. Also understand it properly.
- Interference of two SHMs may not be SHM so first check for it before solving further.
Tips/guidelines–
- First understand small parameters of SHM and how they relate to each other because it can solve more than half problem easily.
- Visualize problems with circular motion, it’ll be easier to solve.
- In problems on oscillations due to spring there can be more than one spring arrangement. So use series or parallel equivalent of springs to make it simpler.
- Prepare theory part of damped oscillations well. It’s important with respect to exams.
- Sometimes SHM is combined with kinematics problems so use of energy methods may be useful.
- Focus mainly on oscillation due to spring, resonance systems and problems on force law here.
Above we discussed abut oscillations mainly SHM. We saw about its properties, parameters and superposition of them. We looked its examples also. Along this, we discussed damped, forced oscillations and resonance systems. So go ahead.
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(Image Source :https://en.wikipedia.org/wiki/Pendulum)
