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.

(A) Draw a neat diagram showing the spring, mass, amplitude, equilibrium position, and both

ends of the oscillation.

(B) Calculate the period.

(C) Calculate the maximum speed.

(D) Use the conservation of energy and the result of part (C) to calculate the spring constant.

(E) Calculate the maximum acceleration.

(F) Calculate the total energy.

(G) Write down the position as a function of time. [like: x(t) = A

cos(2πft)]

(H) Calculate the position at t=4.0 s.

(I) Calculate the speed at t=4.0 s using the conservation of energy.

The figure below shows a history graph at x=2 m of a wave moving to the right at 1 m/s. Draw a

snapshot graph of the wave at t=1 s.

y (cm) -2-2 3/4 5 6

(A) Draw a history graph first, then explain briefly the procedure to draw the snapshot graph.

(B) Draw a neat snapshot graph with correct units and labels.

Answer 1

m = 2 wg w = squareroot k/m 2 phi w = squareroot k/m v = No. of oscillation/time taken = 10/12 Hz \r\n [(2 phi) (10/12)]^2 = k/m 4 phi^2 (100/144) times (0.2) = k k = 5.483 N/m amplitude = 10 cm (A) (B) = T = 12 sec/10 rev = 1.2 sec/rev (c) calculate the max speed V_q max = A w = (10 times 10^minus m) (2 phi/1.2) = 5.235 times 10^minus 1 m/sec = 0.5235 m/sec (d) max Energy = 1/2 m V^2_max = 1/2 (0.2) (0.5235)^2 = 27.4 mJ \r\n PE_max = 1/2 KA^2 = mv^2_max 1/2 k(0.1)^2 = 27.4 times 10^minus 3 J k = 2 times 27.4 times 10^minus 3 times 100/0.01 = 54.8 times 10^minus 1 = 5.48 N/m E) max acc. = Aw^2 = (0.1) (2 phi/1.2)^2 = 2.74 m/sec^2 (F) total Energy = 27.4 mJ