Question

versity - S ASH Activities and Due Dates > HW 11: Oscillations Assignment Score: 743/1000 Resources Feedback Try Again Question 8 of 10 > Attempt 1 - A particle with mass 1.01 kg oscillates horizontally at the end of a horizontal spring. A student measures an amplitude of 0.887 m and a duration of 121 s for 72 cycles of oscillation. Find the frequency, f. the speed at the equilibrium position, Umax, the spring constant, k, the potential energy at an endpoint, Umax, the potential energy when the particle is located 34.3% of the amplitude away from the equilibrium position, U, and the kinetic energy, K, and the speed, w, at the same position.

Answer 1

A)

Time, T = 121/72 = 1.68 sec

Frequency, f = 1/T = 0.60 Hz

B)

Speed, v = A (2 pi f)

v = 0.887 x (2 pi x 0.60) = 3.32 m/s

C)

Spring constant, k = mw^2

k = 1.01 x (2 pi x 0.6)^2 = 14.35 N/m

D)

Potential energy, U = 0.5 kA^2

U = 0.5 x 14.35 x 0.887^2 = 5.65 J

E)

Potential energy, U = 0.5 kx^2

U = 0.5 x 14.35 x (0.343 x 0.887)^2 = 0.66 J

F)

Kinetic energy, E = 5.65 - 0.66 = 4.98 J

G)

Velocity, v = sqrt(2E/m)

v = sqrt(2 x 4.98/1.01) = 3.14 m/s

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