Question

You have a 0.16 ?kg block on a 18 ?N/m spring that oscillates up and down. How often do you need to push the block upward when it passes the bottom of its motion to increase the amplitude of its vibrations? Answer is f= 1.7Hz

Answer 1

To increase the amplitude of its vibrations, you need to push the block upward when it passes the bottom of its motion in hte same frequency as that of the frequency of the vibration itself.

Angular Frequency of the vibration is (spring constant/mass)^1/2 = (18/0.16)^1/2 = 10.61 /s

So, Frequency of the vibration is f = Angular Frequency of the vibration / 2*pi = 10.61/2*3.14 = 1.7 /s =  1.7Hz

So, the Frequency with which you need to push the block upward when it passes the bottom of its motion to increase the amplitude of its vibrations is  f =  1.7Hz