Simple Harmonic Motion (SHM) is a periodic motion the body moves to and fro about its mean position. The restoring force on the oscillating body is directly proportional to its displacement and is always directed towards its mean position.
Q. What is the equation of SHM?
Equations
| Equation | Symbols | Meaning in words |
|---|---|---|
| x ( t ) = A cos ( 2 π f t ) x(t) = A/cos(2 /pi f t) x(t)=Acos(2πft) | x x x is displacement as a function of time, A is amplitude, f is frequency, and t is time | Displacement as a function of time is proportional to amplitude and the cosine of 2 π 2/pi 2π times frequency and time |
Q. Is every oscillatory motion is SHM?
And, the simple harmonic motion is always oscillatory. Periodic motion examples are the motion of the hands of a clock, the motion of the wheels of a car, etc. Simple harmonic motion examples: the motion of a pendulum, motion of a spring, etc. Learn the difference between Periodic and Oscillatory Motion here.
Q. What is acceleration at mean position in SHM?
Simple Harmonic Motion or SHM is defined as a motion in which the restoring force is directly proportional to the displacement of the body from its mean position. The acceleration of a particle executing simple harmonic motion is given by, a(t) = -ω2 x(t).
Q. Why acceleration is Max at extreme position in SHM?
Acceleration in SHM When the displacement is maximum, the acceleration is maximum, because the spring applies maximum force; the force applied by the spring is in the opposite direction as the displacement.
Q. What is the value of acceleration at mean position in SHM?
Solution: At mean position, x =0. ∴ acceleration = -ω2 x = -ω2 × 0 = 0. Therefore, the value of acceleration at the mean position is minimum and it is zero.
Q. Why in SHM acceleration is zero when velocity is greatest?
Answer : In simple harmonic motion (S.H.M.) the acceleration of a body is directly proportional to the displacement . Therefore, it is zero when it is at equilibrium position i.e velocity is maximum at that position. Hence, the acceleration is zero at the equilibrium position when the velocity is greatest .
Q. At what point is the velocity maximum?
Choose a point just to the left of the extremum and another point just to the right. If acceleration is negative to the left and positive to the right, the point is a minimum velocity. If acceleration is positive to the left and negative to the right, the point is a maximum velocity.
