A particle executes simple harmonic motion with an amplitude of 4 cm . At the mean position, velocity of the particle is 10 cm s - 1 . The distance of the particle from the mean position when its speed becomes 5 cm s - 1 is α cm , where α = ______.

Step-by-step solution

The formula to calculate the velocity of the particle at the mean position is given by V = A ω . . . 1 From equation (1), it follows that 10 = 4 × ω ⇒ ω = 5 2 rad s - 1 The formula to calculate the velocity of the particle at any instantaneous position x can be expressed as v = ω A 2 - x 2 . . . 2 From equation (2), it follows that 5 = 5 2 4 2 - x 2 ⇒ x 2 = 16 - 4 = 12 ⇒ x = 12 cm Hence, α = 12 .