A spring hangs from the ceiling with an unstretched length of xo = 0.97 m. A m = 7.5 kg block is hung from the spring, causing the spring to stretch to a length X1 = 1.16 m. Find the length x2 of the spring when a m2 = 2.9 kg block is hung from the spring. For both cases, all vibrations of the spring are allowed to settle down before any measurements are made. m, X2 = 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.
![**Problem Description:**
A spring hangs from the ceiling with an unstretched length of \( x_0 = 0.97 \, \text{m} \). A block with mass \( m_1 = 7.5 \, \text{kg} \) is hung from the spring, causing the spring to stretch to a length \( x_1 = 1.16 \, \text{m} \).
Find the length \( x_2 \) of the spring when a block with mass \( m_2 = 2.9 \, \text{kg} \) is hung from the spring. For both cases, all vibrations of the spring are allowed to settle down before any measurements are made.
**Diagrams Explanation:**
- **First Diagram:** Shows the spring hanging vertically with no load, depicting its unstretched length \( x_0 \).
- **Second Diagram:** Illustrates the spring with a block of mass \( m_1 \) hanging from it, stretched to length \( x_1 \).
- **Third Diagram:** Depicts the spring with a block of mass \( m_2 \) hanging from it, intended to stretch to the unknown length \( x_2 \).
**Solution:**
\[ x_2 = \, \underline{\hspace{3cm}} \, \text{m} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa24f8f00-6441-4c6e-94c3-ec33b4d7128f%2F035445db-4e41-4ca8-8310-746988d50592%2Febv2h1_processed.png&w=3840&q=75)
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