If simple harmonic motion is represented by x = A cos(ωt + φ), th
| If simple harmonic motion is represented by x = A cos(ωt + φ), then the maximum and minimum values of this function are ______________.
A. ± ω
B. ± A
C. ± φ
D. ± t
Please scroll down to see the correct answer and solution guide.
Right Answer is: B
SOLUTION
CONCEPT:
- Simple Harmonic Motion (SHM): Simple harmonic motion is a special type of periodic motion or oscillation where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement.
Force (F) = - k x
Where k = restoring force, x = distance from the equilibrium position, F = force it experiences towards mean position
- Example: Motion of an undamped pendulum, undamped spring-mass system.
EXPLANATION:
- Simple harmonic motion is represented by
⇒ x = A cos(ωt + φ)
- As we know that the maximum value of cos = 1, therefore
⇒ x = A
- Similarly, the minimum value of cos = -1, therefore
⇒ x = -A
- The maximum and minimum values of this function are ± A.
