Question

Two systems are in oscillation: a simple pendulum swinging back and forth through a very small angle and a block oscillating on a spring. The block-spring system takes twice as much time as the pendulum to complete one oscillation. What could be done to make the two systems oscillate with the same period

Answer 1

Answer:

Here to make the two systems oscillate with same period either decrease the mass of the block system to one fourth or increase the length of the string to four times

Explanation:

we know that time period of block spring system is  $2\pi\sqrt{\frac{m}{k} }$

   where m = mass of the block

              k= spring constant

      and also time period of simple pendulum making small oscillations  is $2\pi\sqrt{\frac{l}{g} }$

      where l = length of the pendulum    

                 g = acceleration due to gravity

   so here to make time period of the both systems to be same either we can decrease the block system time period to its half or double the time period of the pendulum.

 To decrease the time period of block spring system to half its value from above equation we need to decrease the mass of the block to one fourth

 and to increase the time period of the pendulum we need to increase length by four times .