In the right figure, block 2 of mass 2.0 kg oscillates on the end of a spring in SHM with a period of 20 ms. The block's position is given by x = 1 cm · cos(wt + π/2). Block 1 of mass 4.0 kg slides toward block 2 with a ve- locity of magnitude 6.0 m/s, directed along the spring's length. The two blocks undergo a completely inelastic collisio duration of the collision is much less than the period of motion a) Determine the spring constant k 1
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.
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In the right figure, block 2 of mass 2.0 kg oscillates on
the end of a spring in SHM with a period of 20 ms. The
block's position is given by x = = 1 cm · cos(wt + π/2).
Block 1 of mass 4.0 kg slides toward block 2 with a ve-
locity of magnitude 6.0 m/s, directed along the spring's
length. The two blocks undergo a completely inelastic collision at time t'
duration of the collision is much less than the period of motion.)
=
k
00000
5.0 ms. (The
a) Determine the spring constant k.
b) Determine the position of block 2 at the instant of the collision t'.
c) What is the velocity of block 2 at the instant of the collision t'?
d) Determine the velocity v' of block 1 and 2 right after the collision.
e) What types of energy are present right after the collision? Calculate their values.
f) What is the amplitude of the SHM after the collision?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd6070c27-0824-4884-a918-195c8f609349%2F9a43c7c5-ddca-47c0-9fab-feb73780c222%2Ft67xmbi_processed.png&w=3840&q=75)
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