How Long Until the Oscillator's Energy Halves?

AI Thread Summary
The discussion focuses on calculating the time it takes for the energy of an oscillating mass-spring system to reduce to half its initial value due to a frictional effect. The period of oscillation is given as 0.820 seconds, and the amplitude decreases by a factor of 0.985 with each complete oscillation. A proposed method involves using the relationship between amplitude and energy, where the energy is proportional to the square of the amplitude. The suggested approach is to determine the new amplitude after several oscillations and then calculate the time based on the period. The conversation emphasizes finding a straightforward solution without complex calculus.
NAkid
Messages
70
Reaction score
0

Homework Statement


A mass M is suspended from a spring and oscillates with a period of 0.820s. Each complete oscillation results in an amplitude reduction of a factor of 0.985 due to a small velocity dependent frictional effect. Calculate the time it takes for the total energy of the oscillator to decrease to 0.500 of its initial value.


Homework Equations





The Attempt at a Solution



Tried .985^t = .5, then t = log(.5)/log(.985) but this didn't work... any other suggestions?
 
Physics news on Phys.org
NAkid said:
... any other suggestions?

Try a direct and simple approach, without calculus. The total E of the spring is (1/2)kA^2, where A is the amplitude. For the energy to become E/2, you can find A.

After each oscillation, it becomes cA, where c = 0.985. If it starts out with amplitude A0 and energy E0, then you can calculate after how many swings the energy becomes E0, by using the above mentioned process. Then find the time.
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Estimating damped harmonic oscillator parameters from this plot of the oscillations
Replies
9
Views
2K
Oscillating horizontal mass attached to a spring with Friction
Replies
1
Views
2K
Finding the damping force for a critically damped oscillator
Replies
2
Views
2K
Collisions in a harmonic oscillator
Replies
18
Views
3K
Damped harmonic motion
Replies
3
Views
596
How to calculate quality factor for RLC circuit?
Replies
6
Views
1K
Finding Amplitude of spring oscillation after damping
Replies
15
Views
5K
Damped Oscillators: Homework Solution
Replies
9
Views
2K
What is the value of b for a damped harmonic oscillator with given parameters?
Replies
2
Views
2K
Solve questions on oscillations and kinetic energy
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top