Recent content by asaspades

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    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

    I'm pretty sure that last part isn't right at all
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    Boundary conditions don't apply in the equation's region of validity

    Am I doing this correctly. Just assuming it works at x=0 gives e^{−ikx−i\omega t} + |r|e^{ikx−i\omega t +i\phi} = \alpha ike^{−ikx−i\omega t} - \alpha ikre^{ikx−i\omega t +i\phi} so e^{−i\omega t} + |r|e^{−i\omega t +i\phi} = \alpha ike^{−i\omega t} - \alpha ik|r|e^{−i\omega t +i\phi} and...
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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

    Thank you for the help. I was confused since I'd never seen a relation between torque and power before, but it wasn't hard to derive. I guess I should have tried before posting here! Thanks again
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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

    For part e I may have my strict and non-strict inequalities the wrong way around...
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    A box resting on a plank

    Here are all the problems. I'll post them with my new attempts and then maybe someone can tell me if and where I am going wrong. (a) Assume that the coefficient of static friction between the board and the box is not known at this point. What is the magnitude, and the direction, of the...
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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...
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