Calculations with SHM
Equations
\[x=A\cos(\omega t)$$
$$a=-\omega^2x$$
$$a_{\text{max}}=\omega^2A$$
$$v=^+_{-}\omega \sqrt{ A^6-x^2 }$$
$$v_{\text{max}}=\omega A\]
A pendulum moving with SHM has an angular frequency of 1.5rad\(^{-1}\) and an amplitude of 1.6m.
- Find acceleration when displacement is 1.6.
\(a=-\omega^2x\)
\(1.5^2=2.25\)
\(ans\times1.6=3.6\) - How long does it take to complete 15 oscillations?
\(\frac{\omega}{2\pi}=0.2387\)
\(\frac{1}{\text{ans}}=4.188\)
\(15\times \text{ans}=62.83=20\pi\)
A mass attached to a spring oscillates with SHM. It has a period of 0.75 s, and moves with speed 0.85 ms\(^{-1}\) when passing through its equilibrium position.
- What is the amplitude of its oscillation?
\(v_{\text{max}}=0.85\)
\(T=0.75\)
\(\omega=2\pi \times \frac{1}{0.75}\)
\(\frac{0.85}{\frac{8}{3}\pi}=0.10146\)
\(\therefore A=0.10146\)