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A block of mass m is attached to a massless spring of force constant k, the other end of which is fixed from the wall of a truck as shown in the figure. The block is placed on the smooth horizontal surface of the truck and initially the spring is unstretched. Suddenly the truck starts moving towards left with a constant acceleration $a_{0}$ . As seen from the truck,

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the particle will execute SHM

the energy of oscillation will be $\frac{m^{2} a_{0}^{2}}{k}$

the amplitude of oscillation will be $\frac{m a_{0}}{k}$

the time period of oscillation will be $2 π \sqrt{\frac{m}{k}}$

answer is A, B, C.

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Detailed Solution

The situation is similar to the vertically loaded spring suddenly released from relaxed position.

$T = 2 π \sqrt{\frac{m}{k}} m a_{0} = k A \Rightarrow A = \frac{m a_{0}}{k} E = \frac{1}{2} m ω^{2} A^{2} = \frac{1}{2} m \cdot \frac{k}{m} \cdot \frac{m^{2} a_{0}^{2}}{k^{2}} = \frac{1}{2} \cdot \frac{m^{2} a_{0}^{2}}{k}$

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