1. A mass of 2.00 kg is attached to a horizontal spring, pulled to an initial po

Question

1. A mass of 2.00 kg is attached to a horizontal spring, pulled to an initial position of +6.00 cm and thrown with an initial velocity of +25.2 cm/s. The spring/mass system is observed to have a period of 2.00 seconds. Assuming there is no damping find a) the angular frequency, b) frequency, c) spring constant, d) the amplitude and the phase angle , e) x(1.00s), x(with dot over it) (1.00s), x(with two dots over it) (1.00s), f) the maximum acceleration of the mass and g) the first time the acceleration is maximum.

2. Waves are sent down a 2.00m long string pinned down at both ends setting up standing waves. The equation for these waves is given by, y(x,t) = (0.040m) sin (2pi multiplied by x) cos (200pi mulitplied by t)

Find a) the amplitude of the original waves sent, b) frequency, c) wavelength, d) what harmonic this is, e) the position of nodes and f) the position of the antinodes.

Explanation / Answer

a) w = 2pi/T = 2*3.14/2 = 3.14s

b) f = 1/T = 1/2 = 0.5 Hz

c) K = m*w^2 = 2*3.14*3.14 = 19.7192 N/m

d) E = 0.5*k*x^2 + 0.5*m*v^2 = 0.5*k*A^2

k*A^2 = kx^2 + mv^2

A^2 = x^2 + w^2*v^2

A^2 = (0.06*0.06)+(3.14*3.14*0.252*0.252)

A = 0.793 m <---------answer

e) x = A*coswt

v = A*w*sinwt

V = 0

f) a = -w^2*A*coswt = 7.82 m/s^2

f) a = -w^2*A = 7.82 m/s^2

g)at t = 0

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

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