A mass of 0.26 kg is attached to a spring and set into oscillation on a horizont

Question

A mass of 0.26 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by x(t) = (0.36 m)cos[(20 rad/s)t]. Determine the following. (c) position of the mass after it has been oscillating for one half a period m (d) position of the mass one-third of a period after it has been released m (e) time it takes the mass to get to the position x = 0.10 m after it has been released s

You have a two-wheel trailer that you pull behind your ATV. Two children with a combined mass of 76.2 kg hop on board for a ride through the woods and the springs (one for each wheel) each compress by 5.37 cm. When you pull the trailer over a tree root in the trail, it oscillates with a period of 1.94 s. Determine the following.(b) mass of the trailer

Explanation / Answer

In general, x(t) = A cos(t - ), where A is the amplitude, is the angular frequency, and is some phase shift


(c)
x(0.5 s) = (0.36 m)cos[(20 rad/s)(0.5 s)]
x(0.5 s) = 0.35 m

(d)
x(t) = (0.36 m)cos[2/3]
x(t) = 0.35 m

(e)
-0.10 m = (0.36 m)cos[(20 rad/s)(t)]
cos(20t) = -0.277
20t = 106.08
t = 5.30 s

2.

mass of the trailer
T = 1.94 s
f = 1/T = 0.5155 Hz
f = /2
= 2f = 3.2388 rad/s
² = k/m

{ force constant of the springs
k = F/x
k = 76.2(9.81) / 0.0537
k = 13920.33 N/m }
m = k / ² = 13920.33 / 3.2388² = 1327.03 kg

so trailer mass is
m = 1327.03 - 76.2 = 1250.8kg

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