n object attached to a spring undergoes simple harmonic motion modeled by the differential quation m dt? + kx O where x(t) is the displacement of the mass (relative to equilibrium) at ime t, m is the mass of the object, and k is the spring constant. A mass of 14 kilograms stretches he spring 0.9 meters. Jse this information to find the spring constant. (Use g = 9.8 meters/second2) k =
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
![Question 1
An object attached to a spring undergoes simple harmonic motion modeled by the differential
equation m
dt
+ kx = 0 where x(t) is the displacement of the mass (relative to equilibrium) at
12]
2
time t, m is the mass of the object, and k is the spring constant. A mass of 14 kilograms stretches
the spring 0.9 meters.
Use this information to find the spring constant. (Use g = 9.8 meters/second-)
k =
The previous mass is detached from the spring and a mass of 4 kilograms is attached. This mass is
displaced 0.3 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)
leave unknown constants in your equation.
G, cos(wt) + C2 sin(wt). Do not
a(t)
డల
Rewrite the equation of motion in the form x(t) = A sin(wt + o), where 0 <¢ < 2T. Do not
leave unknown constants in your equation.
x(t) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F98a85d3f-1221-4cd9-b5c2-c225eed9a46f%2F597b3559-2475-40fa-960d-a7a312d316c0%2Flsxs548_processed.jpeg&w=3840&q=75)
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