A 0.400-kg object attached to a spring with a force constant of 8.00 N/m vibrates in simple harmonic motion with an amplitude of 11.8 cm. (Assume the position of the object is at the origin at t = 0.) (a) Calculate the maximum value of its speed. Have you calculated the angular velocity? You almost always need this quantity for problems involving simple harmonic motion. cm/s (b) Calculate the maximum value of its acceleration. cm/s? (c) Calculate the value of its speed when the object is 7.80 cm from the equilibrium position. cm/s
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 0.400-kg object attached to a spring with a force constant of 8.00 N/m vibrates in simple harmonic motion with an amplitude of 11.8 cm. (Assume the position of the object is at the origin at t = 0.)
(a) Calculate the maximum value of its speed.
[Text Box] cm/s
Have you calculated the angular velocity? You almost always need this quantity for problems involving simple harmonic motion. cm/s
(b) Calculate the maximum value of its acceleration.
[Text Box] cm/s²
(c) Calculate the value of its speed when the object is 7.80 cm from the equilibrium position.
[Text Box] cm/s
(d) Calculate the value of its acceleration when the object is 7.80 cm from the equilibrium position.
[Text Box] cm/s²
(e) Calculate the time interval required for the object to move from x = 0 to x = 5.80 cm.
[Text Box] s](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0d31ea21-51a6-4893-9fcb-4fc7e3b87aa7%2F8aa2ac80-b829-4385-b5f4-2cec7be8eb9d%2Fwhko8k8_processed.jpeg&w=3840&q=75)
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