Q10 **Problem Statement:**A mass \( m = 9 \, \text{kg} \) is attached to a spring and allowed to hang in the Earth's gravitational field. The spring stretches \( 2.2 \, \text{cm} \) before it reaches its equilibrium position. If allowed to oscillate, what would be its frequency?**Options:**- \( 0.30 \, \text{Hz} \) - \( 1.7 \, \text{Hz} \)- \( 3.4 \, \text{Hz} \)- \( 5.1 \times 10^{-3} \, \text{Hz} \)**Explanation:** To calculate the frequency of oscillation, the spring constant \( k \) can be determined using Hooke's Law \( F = kx \), where \( F \) is the force due to gravity (\( F = mg \)) and \( x \) is the spring's extension. Once \( k \) is found, the frequency of oscillation \( f \) can be calculated using the formula \( f = \frac{1}{2\pi} \sqrt{\frac{k}{m}} \). This problem involves understanding the relationship between mass, spring constant, and oscillation frequency.

Name: Q10 **Problem Statement:**A mass \( m = 9 \, \text{kg} \) is attached
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Description: Q10 **Problem Statement:**A mass \( m = 9 \, \text{kg} \) is attached to a spring and allowed to hang in the Earth's gravitational field. The spring stretches \( 2.2 \, \text{cm} \) before it reaches its equilibrium position. If allowed to oscillate,

Given data: A mass is attached to the spring, hang in earths gravitational field Mass (m) = 9 kg…

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A mass m = 9 kg is attached to a spring and allowed to hang in the Earth's gravitational field. The spring stretches 2.2 cm before it reaches its equilibrium position. If allowed to oscillate, what would be its frequency? 0.30 Hz 017Hz O 3.4 Hz ( 5.1x 103 Hz

A mass m = 9 kg is attached to a spring and allowed to hang in the Earth's gravitational field. The spring stretches 2.2 cm before it reaches its equilibrium position. If allowed to oscillate, what would be its frequency? 0.30 Hz 017Hz O 3.4 Hz ( 5.1x 103 Hz

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Chapter1: Units, Trigonometry. And Vectors

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Concept explainers

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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Q10

**Problem Statement:**

A mass \( m = 9 \, \text{kg} \) is attached to a spring and allowed to hang in the Earth's gravitational field. The spring stretches \( 2.2 \, \text{cm} \) before it reaches its equilibrium position. If allowed to oscillate, what would be its frequency?

**Options:**
- \( 0.30 \, \text{Hz} \)
- \( 1.7 \, \text{Hz} \)
- \( 3.4 \, \text{Hz} \)
- \( 5.1 \times 10^{-3} \, \text{Hz} \)

**Explanation:**

To calculate the frequency of oscillation, the spring constant \( k \) can be determined using Hooke's Law \( F = kx \), where \( F \) is the force due to gravity (\( F = mg \)) and \( x \) is the spring's extension. Once \( k \) is found, the frequency of oscillation \( f \) can be calculated using the formula \( f = \frac{1}{2\pi} \sqrt{\frac{k}{m}} \).

This problem involves understanding the relationship between mass, spring constant, and oscillation frequency.

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