Spring during Christmas? A uniform solid sphere of mass M = 53.7[g] and radius R is hanged by two ideal springs. The first spring has force constant k₁ = 28.6[N/m], while the second spring has a force constant of k2= 19.2[N/m]. When point P is pulled downward with a small displacement y and is then released, the sphere oscillates without slipping. What is the period of small oscillations of the sphere? k₂ M R k₁ P
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.
![Spring during Christmas? A uniform solid
sphere of mass M = 53.7[g] and radius Ris
hanged by two ideal springs. The first spring has
force constant k₁ = 28.6[N/m], while the
second spring has a force constant of
k2 19.2[N/m]. When point P is pulled
downward with a small displacement y and is
then released, the sphere oscillates without
slipping. What is the period of small oscillations
of the sphere?
k₂
Select one:
O 0.0942[s]
0.300[s]
O 0.188[s]
O 0.1333 [s]
M
k₁
P](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f3373ad-27b9-4e71-b087-871ea853e011%2F492e890e-e48d-4708-8789-bc3f7ee25ad7%2Fozhxqz_processed.png&w=3840&q=75)
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