Oscillations of a mass on a spring.

In summary, adding a mass M to a mass m suspended from a spring of constant k results in a period of 3T, where T is the period of the mass m alone. By solving mathematically, it can be determined that M=8m, which is 9 times the mass m.
  • #1
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A mass m suspended from a spring of constant k has a period T. If a mass M is added, the period becomes 3T. Find M in terms of m.T=2pi(m/k)^(1/2)
I know that the period varies as the square root of the mass so the mass M should be 9 times that of m. The answer is M=8m. I don't know why it is 8 instead of 9. Any help would be appreciated.

Thanks
 
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  • #2
Your equation is a bit wrong (typo, maybe?), T=2pi(m/k)^(1/2). Have you worked it out mathematically? You will get M=8m. Remember that the total mass is M + m for when the period is 3T. Try to work it out.
 
  • #3
Nice. Inserting M+m then solving works. Thank you.
 

FAQ: Oscillations of a mass on a spring.

1. What is an oscillation?

An oscillation is a repeated back-and-forth motion around a central point or position. In the context of a mass on a spring, it refers to the movement of the mass as it stretches and contracts the spring.

2. How does a mass on a spring oscillate?

The oscillation of a mass on a spring is caused by the restoring force of the spring. When the mass is displaced from its equilibrium position, the spring exerts a force that pulls the mass back towards the equilibrium position. This causes the mass to oscillate around the equilibrium position.

3. What factors affect the oscillation of a mass on a spring?

The oscillation of a mass on a spring is affected by the mass of the object, the stiffness of the spring, and the amplitude and frequency of the oscillation. The mass and stiffness determine the period, or the time it takes for one complete oscillation, while the amplitude and frequency affect the shape and speed of the oscillation.

4. What is the relationship between the period and frequency of oscillation?

The period and frequency of oscillation are inversely proportional. This means that as the frequency increases, the period decreases, and vice versa. The relationship between the two can be described by the equation T = 1/f, where T is the period and f is the frequency.

5. What are some real-life examples of oscillations of a mass on a spring?

Oscillations of a mass on a spring can be seen in various everyday objects, such as a swinging pendulum, a bouncing pogo stick, or a car's suspension system. They are also used in scientific instruments, such as seismometers for detecting earthquakes and mass spectrometers for analyzing particles.

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