mass of 0.400 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) = (0.700 m)cos[(20.0 rad/s)t]. Determine the following. (a) amplitude of oscillation for the oscillating mass ______ m (b) force constant for the spring ______ N/m (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
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.
A mass of 0.400 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The
(a) amplitude of oscillation for the oscillating mass
______ m
(b) force constant for the spring
______ N/m
(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 = −0.100 m after it has been released
______ s
![A mass of 0.400 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) = (0.700 m) cos[(20.0 rad/s)t]. Determine the following.
(a) amplitude of oscillation for the oscillating mass
m
(b) force constant for the spring
N/m
(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 = -0.100 m after it has been released](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7c560a1a-db76-4fd0-82f5-78bd443b8157%2F54902f8d-8d4b-417c-a9e4-efccb741a14c%2Fak804yn_processed.jpeg&w=3840&q=75)
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I am confused with part (e). I don't understand the steps. How is 1.427 obtained? How is the 20t moved to the left side of the equation, since it is inside the COS() function? I am just not understanding the math. Can you step it through with an explanation at each individual step?
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