A spring-mass system, with mass 150 g, is put into simple harmonic motion, and a

ID: 1837518 • Letter: A

Question

A spring-mass system, with mass 150 g, is put into simple harmonic motion, and a period of 0.25 s is measured with a stopwatch.

a) The spring constant is _______ .

b) If the system is started in motion at a speed of 5.00 m/s from the equilibrium position, the equation of motion for x is _______ .

c) The energy of the system in motion is _______ J.

d) The amplitude of its motion is _______ m

e) The maximum acceleration is _______ m/s2

f) The potential energy when the spring is midway between equilibrium and the amplitude is _______ J

(A) T = 2pi sqrt(m/k)

0.25 = 2pi sqrt(0.150 / k)

k = 94.75 N/m

(B) w = 2pi/T = 2pi/0.25 = 8pi

and v = Vmax cos(w t) = 5 cos(8 pi t) m/s

integrating,

x = (5 / 8 pi ) sin(8 pi t)

x = 0.20 sin(8 pi t) m

= 0.150 x 5^2 /2 = 1.875 J

(D) A = 0.20 m

(E) a_max = kA/m = (94.75 x 0.20)/0.150 = 126 m/s^2

(F)
x = A/2 = 0.10 m

energy = kx^2/2= 94.75 (0.10^2)/2= 0.47 J

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.