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  1. A

    Forced SHM with damping problem

    Homework Statement A mass, m, attached to a spring hangs vertically downwards under gravity. It is subject to a viscous damping force proportional to its velocity. The spring constant is k > 0. A periodic force is applied to the spring and the equation of motion for the mass is \ddot x+...
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    Boundary conditions don't apply in the equation's region of validity

    Homework Statement A tight string lies along the positive x-axis when unperturbed. Its displacement from the x-axis is denoted by y(x, t). It is attached to a boundary at x = 0. The condition at the boundary is y+\alpha \frac{\partial y}{\partial x} =0 where \alpha is a constant. Write the...
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    Acceleration of the tips of wind turbine blades

    Homework Statement A wind turbine has a rotor (its rotating section) which has a moment of inertia I = 1.26 × 10^7 \text{kgm}^2. At peak output, with the rotor completing 0.25 \text{ revolutions per second}, the turbine produces a power of P = 3\text{MW}. The tips of the rotor blades sweep out...
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    Waves on water

    Homework Statement A water wave traveling in a straight line on a lake is described by the equation y(x,t)=(3.75\,\text{cm})\cos(0.450\,\text{cm}^{-1}x+5.40\,\text{s}^{−1}t) where y is the displacement perpendicular to the undisturbed surface of the lake. How much time does it take for one...
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    Hockey stick and puck

    Homework Statement A hockey stick of mass m_{s} and length L is at rest on the ice (which is assumed to be frictionless). A puck with mass m_{p} hits the stick a distance D from the middle of the stick. Before the collision, the puck was moving with speed v_{0} in a direction perpendicular to...
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    A box resting on a plank

    Homework Statement A small box of mass m_{1} resting on a plank, of mass m_{2} and length L, which itself rests on a frictionless, horizontal surface. Both box and board are stationary when a constant force F is applied to the board. Take g to be the acceleration due to gravity and...