Answer:
4.77, approximately 5 cycles per minute
Step-by-step explanation:
For a loaded spring, the frequency of oscillation is given by
[tex]f=\dfrac{1}{2\pi}\sqrt{\dfrac{m}{k}}[/tex]
where [tex]m[/tex]Vis the mass of the load and [tex]k[/tex] is spring constant.
Substituting values in the question,
[tex]f=\dfrac{1}{2\pi}\sqrt{\dfrac{1000}{4000}}[/tex]
[tex]f=\dfrac{1}{2\pi}\sqrt{\dfrac{1}{4}} [/tex]
[tex]f=\dfrac{1}{2\pi}\times\dfrac{1}{2}[/tex]
[tex]f=\dfrac{1}{4\pi}[/tex]
This value is in units of oscillations per second. To convert to oscillations per minute, we divide by [tex]\frac{1}{60}[/tex] or, in essence, multiply [tex]f[/tex] by 60.
Thus, we have
[tex]f=\dfrac{1}{4\pi}\times60[/tex]
[tex]f=\dfrac{15}{\pi}= 4.77 \text{ cycles per minute}[/tex]
