What should you do to the length of the string of a simple pendulum to (a) double its frequency; (b) double its period; (c) double its angular frequency?

Solution 12DQ Introduction We have to discuss how to change the length of a simple pendulum to achieve the given condition. Step 1 (a) The frequency of a simple pendulum is given by f = 2 L Hence we can see that the frequency is inversely proportional to the square root of the length of the pendulum. Hence to double the frequency we have to decrease the length by four times. Step 2 (b) The period of oscillation of simple pendulum is given by T = 2 L g So the period is directly proportional to the square root of the the length of the pendulum. Hence to double the period, we have to increase the length by four times.