Question

Problem #1: 10 points A spring having a spring constant k is placed on a smooth horizontal table and the left end is fixed. A mass of 200 g is attached to the other end of the spring. The mass is pushed 10.0 cm (to the left) against the spring, then released. A student with a stopwatch finds that 10 oscillations take 12.0 s. Draw a neat diagram showing the spring, mass, amplitude, equilibrium position, and both ends of the oscillation. . Calculate the period. Calculate the maximum speed. Use the conservation of energy and the result of part (C) to calculate the spring constant. . Calculate the maximum acceleration. . Calculate the total energy. Write down the position as a function of time. [like: x(t) A cos(2nft)], . Calculate the position at t-4.0 s .Calculate the speed at t-4.0 s using the conservation of energy.

Answer 1

Time required for 10 oscillation = 125 1 oscillation = 1.25 So, time period (T) is = 1.25 angular freg (w) = 2 pi/T = 2 pi/1.2 = 5.23/s Now we know angular freg. W = squareroot k/m = > k = mw^2 k = 200 times (5.23)^2 = 5470.58 dyno/cm Equation describing the motion is, x = A sin wt A = 10 cm/= Amplitude So, dx/dt = V = Aw cos wt = speed speed is max at t = 0 So, V_max = Aw cos 0 = Aw = 10 times 5.23 cm/s = 52.3 cm/s therefore total energy (E) = 1/2 m (max)^2 = 1/2 times 200 times = 273529 erg 0 position at t = 4s is x(t) = 10 times sin (4 times 5.23) = 8.7 cm therefore speed at 4s is v = Aw times cos (5.23 times 9) = 25.05 cm/s