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A block of mass M= 1 kg resting on a smooth horizontal surface is connected to a horizontal light spring of spring constant K = 6 N/m whose other end is fixed to a vertical wall. Another block of mass m= 0.5 kg is placed over the block M. If the coefficient of friction between the two block is $μ = 0.4$ ,find the maximum KE ( in J) that the system can have for simple harmonic oscillations under the action of the spring.

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Detailed Solution

$\begin{array}{l} μ N = m ω^{2} A \\ ∴ A_{\max} = \frac{μ N}{m ω^{2}} = \frac{(0.4) m . g}{m ω^{2}} \\ = \frac{(0.4) (10)}{(6 / 1.5)} (ω^{2} = \frac{L}{M + m}) \\ = 1 m \\ M a x i m u m K E = \frac{1}{2} K A^{2} = 3 J \end{array}$

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