Explanation :
(1) No. of jumping jacks, [tex]n=120[/tex]
time, [tex]t=6\ minutes=360\ sec[/tex]
So, frequency is [tex]f=\dfrac{n}{t}[/tex]
[tex]f=\dfrac{120}{360\ sec}[/tex]
[tex]f=0.33 Hz[/tex]
(2) The quarter spins 10 times every seconds
So, frequency [tex]f=10\ Hz[/tex]
and the period of one cycle is, [tex]t=\dfrac{1}{10\ Hz}[/tex]
[tex]t=0.1\ sec[/tex]
(3) mass of block, [tex]m=1.3\ Kg[/tex]
force constant of spring, [tex]K=250\ N/m[/tex]
Time period of oscillations is given by :
[tex]T=2\pi \sqrt{\dfrac{m}{k}}[/tex]
[tex]T=2\pi \sqrt{\dfrac{1.3\ Kg}{250\ N/m}}[/tex]
So, [tex]T=0.45\ sec[/tex]
Frequency, [tex]F=\dfrac{1}{time\ period}[/tex]
[tex]F=\dfrac{1}{0.45\ sec}[/tex]
[tex]F=2.22\ Hz[/tex]
