When a spring is relaxed, it has a length Lo= 18.0 cm. a. (FRC.4) If 1.8 N force is required to stretch the spri Z= 21.0 cm, what is the spring constant k of the
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.
![**2. Spring Mechanics**
When a spring is relaxed, it has a length \(L_0 = 18.0 \, \text{cm}\).
**a.** (FRC.4) If a force of 1.8 N is required to stretch the spring to a length \(|\vec{L}| = 21.0 \, \text{cm}\), what is the spring constant \(k\) of the spring?
**b.** (FRC.4) A 0.25 kg mass is attached to a spring, and the other end is attached to a post on a frictionless table so that the block can slide horizontally on the surface. The spring is compressed by \(|\vec{s}| = 5.0 \, \text{cm}\) and released from rest at \(t=0 \, \text{s}\).
What is the spring force, \(\vec{F}_p\), when the spring is compressed 5.0 cm, as shown in the diagram?
*Diagram Description:*
The diagram depicts a spring attached to a mass on a frictionless table, compressed to 5.0 cm. The spring is indicated with a coil, and the compressive force is shown as an arrow pushing to the left, labeled \(\vec{L}\). The initial relaxed length \(L_0\) of the spring is also marked.
**c.** (COM.1) If the mass is released from rest from \(\vec{L} = (13.0, 0, 0) \, \text{cm}\) at \(t=0 \, \text{s}\), what is the momentum of the mass after 0.01 s? Assume the force is nearly constant on a 0.01 s timestep.
**d.** (COM.1) What is the position \(\vec{L}\) of the mass at \(t=0.01 \, \text{s}\)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F13d2fa52-7679-4dbf-8ccf-e0669bc97f10%2F447641b4-6018-4088-9f8b-36784ba4f67c%2Fgzhetv9_processed.png&w=3840&q=75)
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Given:-
a)
it has a length Lo= 18.0 cm = 0.18 m
The force on the spring F = 1.8 N
The force is required to stretch the spring to a length L = 21.0 cm= 0.21 m
So the distance of the spring d = 0.21-0.18 = 0.03 m
Now The spring force is given as
So the spring constant is 60 N/m
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