Did you know that simplest form of the wave is sinusoidal in nature?
The sinusoidal wave motion corresponds to Simple Harmonic Motion (SHM). SHM is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position. SHM is observed as a repetitive, back and forth motion.
The motion which is repetitive and periodic in nature is said to be a simple harmonic motion. Due to the presence of restoring force the body oscillates in an SHM. Under the action of restoring force, the body is subjected to acceleration, making it cross the rest position due to inertia. Restoring force is also responsible for pulling back the object to the equilibrium state.
Applications Of Simple Harmonic Motion
Pendulum Clock
Clock in early days featured a large pendulum that oscillated and was also a decorative addition. Time-keeping in pendulum clock is done by the quartz crystal. To ensure the correct time, the motion of the crystal or pendulum in the clock must be periodic in nature.
Due to the Simple Harmonic Motion, the oscillation of the pendulum is said to be periodic. Periodic motion is responsible to keep up the time in the clock. It is necessary to keep the pendulum independent of the amplitude of oscillation.
Pendulum Clock
Hearing
Sound is sensed or heard due to the presence of SHM in nature. Sound waves generated in the environment travel through the air and reach the eardrum. Soundwaves cause the eardrum to vibrate when it receives the sound signal. This signal is transmitted to the brain, which then translates these signals into meaningful sounds. Hence, we are able to identify the sound.
Musical Instruments
Sound is produced due to oscillations of the air and the string-based instruments like guitar, violin produces a sound due to bowing or plucking the string. The force applied over the string makes it oscillate and produce sound. The vibration produced in the string or body of the instrument generates standing waves, which produces sound.
Spring
Simple harmonic motion is experienced by a spring. Consider a spring fixed at one end. When there is no force applied to it, the spring is at an equilibrium position. If we pull spring outwards, there is a force exerted by the string that is directed towards the equilibrium position. If inward force is applied to the spring, it moves it towards the equilibrium position.
We can observe that irrespective of inward/outward force on the spring, it is drawn towards the equilibrium position. This force is called the restoring force.
F = displacement of the spring from the equilibrium position be x.
Hence, the restoring force is given by
F= – kx
The negative sign represents the force acting in the opposite direction.
k = force constant.
SI unit = N/m.
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