Question

13. A type of cuckoo clock keeps time by having a mass bouncing on a spring, usually something cute like a cherub in a chair. What force constant is needed to produce a period of 0.500 s for a 0.0150-kg mass?

The answer is 2.37N/m but please show all of your steps.

Answer 1

• Mass=m=0.015kg
• Time=T=0.500s
• Force constant is k

Lets check

$\\ \rm\rightarrowtail T=2\pi \sqrt{\dfrac{m}{k}}$

$\\ \rm\rightarrowtail 0.5=2\pi\sqrt{\dfrac{0.015}{k}}$

• Square on

$\\ \rm\rightarrowtail 0.25=4\pi^2 {\dfrac{0.015}{k}}$

$\\ \rm\rightarrowtail k=\dfrac{4(3.14)^2(0.015)}{0.25}$

$\\ \rm\rightarrowtail k=\dfrac{0.5916}{0.25}$

$\\ \rm\rightarrowtail k=\dfrac{0.591576}{0.25}$

$\\ \rm\rightarrowtail k\approx 2.37N/m$