A block is hung from a vertical spring with spring constant k = 10N/m. Perturbed

Question

A block is hung from a vertical spring with spring constant k = 10N/m. Perturbed from its equilibrium point at y = 0, the block oscillates up and down reaching its lowest point every 0.8 seconds. Its speed as it passes the equilibrium position is 0.3 m/s. A.) Obtain the period, angular frequency, and mass of the block. B.) What is the maximum speed of the block as it oscillates? Find the amplitude of the oscillations. C.) Using conservation of energy, calculate the velocity of the block as it moves up through a point 2 cm above the equilibrium position. D.) Calculate the force on the block as it moves up through a point 2 cm above the equilibrium position. E.) If at t = 0 you observe the block at the position and with the velocity found in steps (C) and (D), then what is the phase angle, in radians? Thanks for the help in advance!!

Explanation / Answer

a)T=0.8 sec w=2*pi/T=7.85 rad/s w=sqrt(k/m) m=0.162 kg v(max)=0.3 m/s 0.5*0.162*0.3^2=0.5*0.162*v^2+0.5*10*0.02^2 v=0.255 m/s K*X=mg X=0.158 m F(net)=mg-k*(0.158-0.02)=0.209 N

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