Solving Damped Oscillator: Time to Reduce to 0.50 Energy

In summary, the conversation discusses a problem involving a mass suspended from a spring and oscillating with a period of 0.880 s. The amplitude decreases by a factor of 0.96 per oscillation due to friction, and the goal is to calculate the time it takes for the total energy of the oscillator to decrease to 0.50 of its initial value. The relevant formulas are also mentioned. Additionally, there is a request for an outline for the first question and a mention of a test tomorrow.
  • #1
zhenyazh
56
0
hi,
i am supposed to solve this excerise and i don't even know where to start.

A mass M is suspended from a spring and oscillates with a period of 0.880 s. Each complete oscillation results in an amplitude reduction of a factor of 0.96 due to a small velocity dependent frictional effect. Calculate the time it takes for the total energy of the oscillator to decrease to 0.50 of its initial value.

even the relevant formulas...
 
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  • #2
the same of this one

A 1.05 kg mass is suspended from a spring, with a spring constant of 161.0 N/m. Find the driving frequency which would cause resonance.

all i need is to know where to start from
 
  • #3
hi
could some one give me an outline for the first question?
i am have no idea what to do.
and i have a test
 

FAQ: Solving Damped Oscillator: Time to Reduce to 0.50 Energy

What is a damped oscillator?

A damped oscillator is a system that exhibits oscillatory behavior, but gradually loses energy over time due to damping forces. These forces can include friction, air resistance, or other forms of resistance.

How is the time to reduce to 0.50 energy calculated for a damped oscillator?

The time to reduce to 0.50 energy for a damped oscillator can be calculated using the equation t = (1/ω)d, where t is the time in seconds, ω is the angular frequency in radians per second, and d is the damping ratio.

What factors affect the time to reduce to 0.50 energy for a damped oscillator?

The time to reduce to 0.50 energy for a damped oscillator is affected by the damping ratio, amplitude of oscillation, and the initial energy of the system. Additionally, the presence of external forces or changes in the physical properties of the system can also affect the time to reduce to 0.50 energy.

How can the time to reduce to 0.50 energy be manipulated for a damped oscillator?

The time to reduce to 0.50 energy for a damped oscillator can be manipulated by adjusting the damping ratio, amplitude of oscillation, or initial energy of the system. Additionally, external forces can be applied to speed up or slow down the rate of energy loss.

Why is the concept of a damped oscillator important in science and engineering?

The concept of a damped oscillator is important in science and engineering because it can be applied to a wide range of systems, from mechanical to electrical to biological. Understanding the dynamics of a damped oscillator can help in designing and analyzing systems, as well as predicting how they will behave over time.

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