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Hi These Are Math 307 Differential Questions I Am Stuck With These Can Anyone Help Me?

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3. +-/9 points
My Notes
In each of the questions below, hanging a mass m from a spring stretches the spring L meters from its unloaded length. Calculate the spring constant k, write the differential equation that governs the motion of the undamped mass-spring system, and find the solution that satisfies the initial
conditions specified. Units are mks; gravitational constant is 9.8 m/s2.
m = 0.5 kg and L = 2.4500meters
Initial displacement is 0.9 and initial velocity is 1
k =
kg/s
xquot; +
X =0
x(t)
m = 0.3 kg and
L = 1.0889 meters
Initial displacement is 0.6 and initial velocity is 0.1
k =
kg/s-
xquot; +
X = 0
x(t) =
m = 0.4 kg
and
L = 0.3920 meters
Initial displacement is 0.4 and initial velocity is 0.6
K =
kg/s2
xquot; +
X = 0
x(t) =
+-/6 points
My Notes
A 6 kg mass is attached to a spring with spring constant 1 Nt/m.
What is the frequency of the simple harmonic motion?
radians/second
What is the period?
seconds
Suppose the mass is displaced 0.8 meters from its equilibrium position and released from rest. What is the amplitude of the motion?
meters
Suppose the mass is released from the equilibrium position with an initial velocity of 0.6 meters/sec. What is the amplitude of the motion?
meters
Suppose the mass is is displaced 0.8 meters from the equilibrium position and released with an initial velocity of 0.6 meters/sec.
of the m
meters
What is the maximum velocity?
m/sScience