Question

For the later problem, I do not know how to find the pseudo oscillations or the shift in cos. Show your work for each problem. Thanks!

homework5: Problem 2 Previous Problem List Next 1 point Math 216 Homework homework5, Problem 2 A mass of 625 grams is attached to the end of a spring that is stretched 90 cm by a force of 9 N. At time t = 0 the mass is pulled 1 meters to the right, stretching the spring, and set in motion with an initial velocity of 2 m/s to the left. Find the resulting displacement x(t) of the mass in the form x(t) = C,cos(a01-α), the amplitude and the period of the motion of the mass. (Give all of your answers in units of kg, m and s, and assume that there is no friction.) x(t)= (note that 0 α < 2 amplitude period= 2pi/4 cos t- π)

Answer 1

here,

mass , m = 0.625 kg

F = 9 N when streched , x = 0.9 m

let the spring constant be k

f = k * x

9 = 0.9 * k

k = 10 N/m

let the amplitude be A

using conservation of energy

0.5 * m * v^2 + 0.5 * k * x^2 = 0.5 * k * A^2

0.625 * 2^2 + 10 * 1^2 = 10 * A^2

A = 1.12 m

angular frequency , w = sqrt(k/m)

w = sqrt(10/0.675)

w = 3.85 rad/s

x = A * cos(w*t - alpha)

x = 1 at t = 0

1 = 1.12 * cos(- alpha)

alpha = 152.87 degree = 2.67 rad

then ,

x = 1.12 * ( cos( 3.85 * t - 2.67 ))