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You can find the mass of the object from the force constant and oscillation freq

ID: 2118461 • Letter: Y

Question

You can find the mass of the object from the force constant and oscillation frequency. You can apply a condition for translational equilibrium to the object when it is at its equilibrium position to determine the amount the spring has stretched from its natural length. Finally, use the initial conditions to determine the amplitude and phase constants, and then differentiate this expression to obtain expressions for the x components of the velocity and acceleration. x(t) = cm vx(t) = cm/s ax(t) = m/s2

Explanation / Answer

(a) T=2(pi)(m/k)^1/2 T=1/f so 1/f=2(pi)(m/k)^1/2 m=k/[4(pi)^2 f^2]=1764/[4*9.8*5.45*5.45]=1.4848 kg (b) at equilibrium mg=kx x=mg/k=1.4848*9.8/1764=8.25mm (c) x=A sin(wt) where A=mg/k w=2(pi)f so x=mg/k sin(2(pi)ft) m v=dx/dt=(mg/k)2(pi)f cos(2(pi)ft) m/s a=dv/dt= - (mg/k)[(2(pi)f)^2] sin(2(pi)ft) m/s^2

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