At a given point of time the value of displacement of a simple harmonic oscillator is given as y = A cos 30 ° . If amplitude is 40 cm and kinetic energy at that time is 200 J , the value of force constant 1 . 0 × 10 x N m – 1 . The value of x is _____.

Step-by-step solution

The formula to calculate the kinetic energy K of a particle executing SHM is given by K = 1 2 k A 2 - y 2       . . . 1 Substitute the values of the known parameters into equation (1) and solve to calculate the value of the unknown parameter. K = 1 2 × k × A 2 - A 2 cos 2 30 ° =   1 2 × k × A 2 sin 2 30 ° ⇒ 200 = 1 2 × 1 . 0 × 10 x × 0 . 4 2 × 1 2 2 =   2 × 10 x 100 ⇒ 10 2 = 10 x - 2 ⇒ x - 2 = 2 ⇒ x = 4