Question

Jason knows that the equation to calculate the period of a simple pendulum is t = 2 ⁢ π ⁢ l g , where t is the period, l is the length of the rod, and g is the acceleration due to gravity. he also knows that the frequency (f) of the pendulum is the reciprocal of its period. How can he express l in terms of g and f? a. l = g 4 ⁢ π 2 ⁢ f 2 b. l = g 2 ⁢ π 2 ⁢ f 2 c. l = g 2 ⁢ π ⁢ f 2 d.

Answer 1

To express the length of a simple pendulum in terms of the acceleration due to gravity and frequency, begin with the frequency equation, f = 1/T, and solve for 'l'. The final equation is l = g / (4π^2f^2), which aligns with option (a).

Step-by-step explanation:

The student, Jason, knows the equation for the period (‘T’) of a simple pendulum is T = 2π√(l/g), and the frequency (‘f’) is the reciprocal of period. To express the length ‘l’ in terms of the acceleration due to gravity ‘g’ and frequency ‘f’, we start with f = 1/T. Taking the reciprocal of the period equation and substituting in for f, we get f = 1/(2π√(l/g)). To solve for ‘l’, you square both sides to get rid of the square root, leading to f2 = 1/(4π2l/g). By rearranging the equation to solve for ‘l’, you multiply both sides by ‘4π2l/g and then divide by ‘f2’, which allows you to isolate ‘l’ on one side. The final formula for ‘l’ is l = g / (4π2f2), corresponding to option (a).