Question

Two particles p and q start from origin and execute s.h.m along x-axis with same amplitude but with periods 3 seconds and 6 seconds respectively. the ratio of the velocities of p and q when they are at mean position is

Answer 1

Given: Two particles p and q start from origin and execute s.h.m along x-axis with same amplitude but with periods 3 seconds and 6 seconds respectively.

To find: The ratio of the velocities of p and q when they are at mean position.

Solution:

• Now let the velocity at the mean position be V(max)

• Then V (max) will be equal to:

                V(max) = Aω

• We know that ω = 2π/T

• Now :

                V1 = A2π / T1

                V2 = A2π / T2

• Here A = A1 = A2.

• Now V1 / V2 = T2 / T1 = 6 / 3 = 2 / 1

Answer:

            So the ratio of the velocities of p and q when they are at mean position is 2:1