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
Simple Harmonic Motion
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.
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