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A system consisting of a smooth movable wedge of angle alpha and a block A of mass m are connected together with a massless spring of spring constant k, as shown in the figure. The system is kept on a frictionless horizontal plane. If the block is displaced slighlly from equilibrium and left to oscillate, find the frequency of small oscillations. |
Answer» Solution :Suppose that the relative displacement of the block A w.r.t the WEDGE is X at same time t, and the corresponding displacement of the block along the horizontal is x.. The total energy of the system canbe written as  `E = (1)/(2) M ((DX.)/(dt))^(2) + (1)/(2) m [((dx)/(dt)) cos alpha - ((dx)/(dt))^(2) sin^(2) alpha]` `M ((dx.)/(dt)) = m ((dx)/(dt) cos alpha - (dx.)/(dt))`...(ii) which gives `(dx.)/(dt) = (m)/(M +m) ((dx)/(dt)) cos alpha` and substituting in the equation for total energy gives: `omega = sqrt((k)/(m_("red") cos^(2) alpha + m sin^(2) alpha)) " where " m_("red") = (mM)/(m + M)` |
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