Question

13. A mass of 1 kg undergoes simple harmonic motion with amplitude of 1 m. If the period of the oscillation is 1 s, calculate the internal energy of the system.

Please show all of your work.

Answer 1

first we need omega

• T=1s

Hence

`\\ \rm\rightarrowtail \omega=(2\pi)/(T)=2\pi`

Now

Total energy:-

`\\ \rm\rightarrowtail (1)/(2)m\omega ^2A^2`

`\\ \rm\rightarrowtail (1)/(2)(1)(2\pi)^2(1)^2`

`\\ \rm\rightarrowtail (1)/(2)(4\pi ^2`

`\\ \rm\rightarrowtail 2\pi ^2`

`\\ \rm\rightarrowtail 2(3.14)^2`

`\\ \rm\rightarrowtail 19.72J`