A 25.0 kg child on a swing kicks upward on the downswing thus changing the distance from the pivot point to her centre of gravity from 2.40 m to 2.28 m. What is the difference in the resonant frequency of her swing before the kick and afterwards? Answer to three significant digits.
The time period of the swing is given by T = 2π √ (L / g) The natural or resonant frequency is n = 1/2π √ (g / L)
L = distance of the center of gravity of child from the pivot. g = acceleration due to gravity
1 √9.81 So n1 = --------------- * ------- = 0.3217 times per second 2 * 3.14 √2.40
1 √9.81 So n2 = --------------- * ------- = 0.3301 times per second 2 * 3.14 √2.28 So the increase in the resonant frequency is : 0.0084 times per second = 0.008 / second
