Simple Harmonic Motion - Mass on a spring

In summary, the conversation discusses the calculation of the force constant of a spring with a mass of 0.2kg attached to its lower end, which produces an extension of 0.05m. The subsequent oscillations and maximum acceleration are also mentioned, with the suggestion to use the information provided to calculate the spring constant and analyze the forces on the mass.
  • #1
nokia8650
219
0
A mass 0.2kg attached to the lower end of a light helical spring produces an extension of 0.05m.

Calculate the force constant of the spring.

The mass is pulled down a further 0.02m and released. Calculate the time period of subseuent oscillations and the maximum value of the accelartion during motion. Assume g =10ms^-2.

I am struggling with all parts of the uestion - please can you outline a method for me to follow.

Thanks alot.
 
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  • #2
Would the acceleration be g?

Thanks
 
  • #3
nokia8650 said:
A mass 0.2kg attached to the lower end of a light helical spring produces an extension of 0.05m.

Calculate the force constant of the spring.
Already you have enough information to calculate the spring constant, and then use it to calculate the period and frequency of the motion.

The mass is pulled down a further 0.02m and released. Calculate the time period of subseuent oscillations and the maximum value of the accelartion during motion.
So what's the amplitude of the motion? How does maximum acceleration depend on amplitude? (You can also find the acceleration by analyzing the forces on the mass.)
 

What is Simple Harmonic Motion?

Simple Harmonic Motion is a type of periodic motion in which a system oscillates back and forth around a central equilibrium point with a constant frequency and amplitude. It is commonly observed in systems such as a mass on a spring, a pendulum, or a vibrating guitar string.

What is a mass on a spring?

A mass on a spring is a simple mechanical system consisting of a mass attached to a spring. When the mass is displaced from its equilibrium position, the spring exerts a restoring force that causes the mass to oscillate back and forth around the equilibrium point. This system is commonly used to demonstrate Simple Harmonic Motion.

What factors affect the frequency of a mass on a spring?

The frequency of a mass on a spring is affected by three main factors: the stiffness of the spring, the mass of the object attached to the spring, and the amplitude of the oscillation. Increasing the stiffness or decreasing the mass will result in a higher frequency, while increasing the amplitude will decrease the frequency.

How is the motion of a mass on a spring described mathematically?

The motion of a mass on a spring can be described using the equation x = A cos(ωt + φ), where x is the displacement of the mass from its equilibrium position, A is the amplitude of the oscillation, ω is the angular frequency (2π times the frequency), and φ is the phase angle. This equation is derived from the principles of Simple Harmonic Motion.

What are some real-world applications of Simple Harmonic Motion?

Simple Harmonic Motion has many practical applications in everyday life. Some examples include the movement of a swing, the motion of a piston in an engine, the vibrations of a guitar string, and the motion of a diving board. It is also used in various fields such as engineering, physics, and mathematics to model and analyze different systems and phenomena.

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