A $1.5\,\text{kg}$ mass attached to a spring with a force constant of $20.0\,\text{N/m}$ oscillates on a horizontal, frictionless track. At $t = 0$, the mass is released from rest at $x = 10.0\,\text{cm}$. (That is, the spring is stretched by $10.00\,\text{cm}$.)

Question

A $1.5\,\text{kg}$ mass attached to a spring with a force constant of $20.0\,\text{N/m}$ oscillates on a horizontal, frictionless track. At $t = 0$, the mass is released from rest at $x = 10.0\,\text{cm}$. (That is, the spring is stretched by $10.00\,\text{cm}$.)(a) Determine the frequency of the oscillations.
, (b) Determine the maximum speed of the mass. Where does the maximum speed occur?
, (c) Determine the maximum acceleration of the mass. Where does the maximum acceleration occur?
, (d) Determine the total energy of the oscillating system.
, (e) Express the displacement as a function of time.
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Jason · Accepted Answer

$f = 0.582\,\text{Hz}$
$\;v_{\text{max}} = 0.365\,\text{m/s}\;\text{ at } x=0$
$\;a_{\text{max}} = 1.33\,\text{m/s}^2\;\text{ at } x=\pm0.10\,\text{m}$
$\;E = 0.1\,\text{J}$
$\;x(t)=0.10\,\cos\Big(\sqrt{\frac{20.0}{1.5}}\,t\Big)$

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