Physics - SHM Question with Solution | TestHub

At equilibrium:$k{x}_0=mg\Rightarrow x_0=\frac{mg}{k}=\frac{1\times 10}{500}=0.02\mathrm{m}=2\mathrm{cm}$

Equilibrium is at length 40 + 2 = 42 cm.

The block is released from 45 cm, so amplitude$A=3\mathrm{cm}=0.03\mathrm{m}$and (A) is wrong.

$v_{\max }=\sqrt{\frac{k}{m}}A=\sqrt{500}\times 3=30\sqrt{5}\mathrm{cm}/\sec$so (B) is correct.

$a_{\max }=\frac{k}{m}A=500\times 0.03=15\mathrm{m}/{\mathrm{s}}^2$so (C) is correct.

The block oscillates between lengths 39 cm and 45 cm; the natural length 40 cm lies between these two, where the elastic potential energy is zero, so (D) is correct.