An object attached to a spring undergoes simple harmonic motion modeled by the differential equation m- + kæ = 0 where x(t) is the displacement of the mass (relative to equilibrium) at time t, m is the dt? mass of the object, and k is the spring constant. A mass of 20 kilograms stretches the spring 0.35 meters. Use this information to find the spring constant (use g = 9.81 m/s? as the approximation for acceleration due to gravity). k = The previous mass is detached from the spring and a mass of 9 kilograms is attached. This mass is displaced 0.2 meters above equilibrium and then launched with an initial velocity of 0.5 meters/second. Write the equation of motion in the form x(t) = c1 cos(wot) + c2 sin(wt). Do not leave unknown constants in your equation. Note: Positions below equilibrium are considered positive. æ(t) = Rewrite the equation of motion in the form æ(t) your equation. R cos(wot – 8). Do not leave unknown constants in æ(t) =
An object attached to a spring undergoes simple harmonic motion modeled by the differential equation m- + kæ = 0 where x(t) is the displacement of the mass (relative to equilibrium) at time t, m is the dt? mass of the object, and k is the spring constant. A mass of 20 kilograms stretches the spring 0.35 meters. Use this information to find the spring constant (use g = 9.81 m/s? as the approximation for acceleration due to gravity). k = The previous mass is detached from the spring and a mass of 9 kilograms is attached. This mass is displaced 0.2 meters above equilibrium and then launched with an initial velocity of 0.5 meters/second. Write the equation of motion in the form x(t) = c1 cos(wot) + c2 sin(wt). Do not leave unknown constants in your equation. Note: Positions below equilibrium are considered positive. æ(t) = Rewrite the equation of motion in the form æ(t) your equation. R cos(wot – 8). Do not leave unknown constants in æ(t) =
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Transcribed Image Text:An object attached to a spring undergoes simple harmonic motion modeled by the differential equation
O where x (t) is the displacement of the mass (relative to equilibrium) at time t, m is the
+ kx =
dt?
mass of the object, and k is the spring constant. A mass of 20 kilograms stretches the spring 0.35 meters.
m
Use this information to find the spring constant (use g = 9.81 m/s? as the approximation for acceleration
due to gravity).
k =
The previous mass is detached from the spring and a mass of 9 kilograms is attached. This mass is displaced
0.2 meters above equilibrium and then launched with an initial velocity of 0.5 meters/second. Write the
equation of motion in the form x(t)
equation.
= cq cos(wot) + c2 sin(wot). Do not leave unknown constants in your
Note: Positions below equilibrium are considered positive.
x(t) =
Rewrite the equation of motion in the form (t) = Rcos(wot – 8). Do not leave unknown constants in
your equation.
æ(t)
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