Determine (i) the frequency of oscillations, (ii) maximum acceleration of the mass, and (iii) the maximum speed of the mass.
$\upsilon=\frac{1}{\text{T}}=\frac{1}{2\pi}\sqrt{\frac{\text{k}}{\text{m}}}$
where, T is time period
$\therefore\ \upsilon=\frac{1}{2\times3.14}\sqrt{\frac{1200}{3}}$
= 3.18m/s
Hence, the frequency of oscillations is 3.18 cycles per second.
$\text{a}=\omega^2\text{A}$
where,
$\omega=$ Angular frequency $=\sqrt{\frac{\text{k}}{\text{m}}}$
A = maximum displacement
$\therefore\ \text{a}=\frac{\text{k}}{\text{m}}\text{A}=\frac{1200\times0.02}{3}=8\text{ ms}^{-2}$
Hence, the maximum acceleration of the mass is 8.0m/s2.
Maximum velocity, $\text{v}_\text{max}=\text{A}\omega$
$=\text{A}\sqrt{\frac{\text{k}}{\text{m}}}=0.02\times\sqrt{\frac{1200}{3}}=0.4\text{ m/s}$
Hence, the maximum velocity of the mass is 0.4m/s.
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