Podcast
Questions and Answers
If the cart's mass is increased while maintaining the same frequency, how will this affect the stiffness of the spring?
If the cart's mass is increased while maintaining the same frequency, how will this affect the stiffness of the spring?
- The stiffness will increase.
- The stiffness will remain unchanged.
- It will depend on the amplitude of oscillation.
- The stiffness will decrease. (correct)
Calculate the stiffness of the spring using the given mass and frequency. What is the stiffness of the spring?
Calculate the stiffness of the spring using the given mass and frequency. What is the stiffness of the spring?
- 32.23 N/m
- 22.05 N/m
- 16.28 N/m (correct)
- 8.14 N/m
Which parameter is directly related to the frequency of oscillation in SHM?
Which parameter is directly related to the frequency of oscillation in SHM?
- Damping coefficient
- Stiffness of the spring (correct)
- Amplitude of the motion
- Mass of the cart
What unit is the stiffness of a spring commonly expressed in?
What unit is the stiffness of a spring commonly expressed in?
Flashcards
Spring Stiffness (k)
Spring Stiffness (k)
The ability of a spring to resist being stretched or compressed. It is the amount of force required to stretch or compress the spring by a unit distance.
Frequency (f)
Frequency (f)
The number of complete oscillations a system makes in one second.
Simple Harmonic Motion (SHM)
Simple Harmonic Motion (SHM)
A type of periodic motion where the restoring force is proportional to the displacement from equilibrium.
Relationship between frequency, mass, and spring stiffness
Relationship between frequency, mass, and spring stiffness
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Hertz (Hz)
Hertz (Hz)
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Study Notes
Harmonic Motion of a Cart Attached to a Spring
- A 5.70 kg cart attached to a spring experiences simple harmonic motion (SHM).
- The frequency of oscillation is 2.61 Hz.
- The goal is to determine the spring stiffness (k).
Relationship Between Frequency and Spring Stiffness
- The frequency (f) of a spring-mass system undergoing SHM is related to the spring stiffness (k) and the mass (m) by the following equation:
- f = (1 / 2π) * √(k / m)
Solving for Spring Stiffness (k)
- Rearranging the equation to solve for k:
- k = (4π² * m * f²)
Calculation
- Substituting the given values:
- m = 5.70 kg
- f = 2.61 Hz
- Performing the calculation:
- k = (4 * π² * 5.70 kg * (2.61 Hz)²)
- Result:
- k ≈ 400 N/m (approximately)
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Description
This quiz focuses on the principles of simple harmonic motion (SHM) of a cart attached to a spring. You will learn how to calculate the spring stiffness using the relationship between frequency and mass. Test your understanding of SHM by solving for spring stiffness with given values.
