Question

The figure gives the position of a 120 g block oscillating in SHM on the end of a spring. The horizontal axis scale is set by ts = 140 ms. What is the maximum kinetic energy of the block?

How many times per second is that maximum reached? (Hint: measuring a slope will probably not be very accurate. Find another approach)

Answer 1

Mass m = 120 g

             = 0.12 kg

Time period T = 140 ms

                       = 0.14 s

Amplitude A = 7 cm     Since from graph

                    = 0.07 m

Angular frequency ω = 2π / T

                                 = 44.87 rad / s

Maximum kinetic energy of the block K.E = ( 1/ 2)m ω ² A ²

                                                                 = 0.5921 J

This maximum is occured 2 times in a period of time.

So, Number of maximums occured in 1 second N = ( 1 s / T ) 2

                                                                            = 7.14 x 2

                                                                            = 14.28

                                                                            ~ 14