Equation of SHM: F=−mω2x Angular frequency =ω Frequency f=2πω Time-period T=ω2π Example: Acceleration-displacement graph of a particle executing SHM is as shown in the figure. Find the time period of oscillation. Solution: In SHM a=−ω2x or a=m−Kx so, from graph −mK=−1(∵slopeis−1) mK=1 Time period =2πKm =2π11 =2π
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Simple Harmonic Motion
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Applications of SHM
Some applications of SHM are:
Simple harmonic motion of a pendulum is used for the measurement of time.
Tuning of the musical instrument is done with the vibrating tuning fork which executes simple harmonic motion.
Wave is a consequence of simple harmonic motion. Study of waves is indirectly the study of simple harmonic motion.
Molecules are in simple harmonic motion. This study is called vibration spectroscopy.
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Characteristics of SHM
A restoring force must act on the body.
Body must have acceleration in a direction opposite to the displacement and the acceleration must be directly proportional to displacement.
The system must have inertia (mass).
SHM is a type of oscillatory motion.
It is a particular case of preodic motion.
It can be represented by a simple sine or cosine function