Maximizing Mass Motion with Minimal Hand Movement

AI Thread Summary
To maximize mass motion with minimal hand movement, the student should oscillate her hand at a frequency of approximately 0.890886 Hz, calculated using the formula involving the spring constant and mass. The correct frequency was derived from the spring constant of 94 N/m and the mass of 3 kg. After the hand movement stops, the mass will gradually come to rest due to damping. To determine how long it takes for the amplitude to reduce to half its maximum, the equation of motion for the damped oscillator should be referenced. Understanding the damping effects is crucial for solving this problem effectively.
wolves5
Messages
52
Reaction score
0
A student gets a 3 kg mass to oscillate up and down on bottom of a light vertical spring by pulling her hand up and down on the top end of the spring. The spring is a real spring with a spring constant of 94 N/m and a damping constant of 0.6 N sec/m.

(a) At what approximate frequency should the student move her hand up and down to get the maximum motion from the mass with the minimum motion of her hand?

The frequency I got was 0.890886 and its correct. I did 2pi times (sq.rt 3/94) and got 1.12247. To get frequency, I did 1/1.12247 and got 0.890886 seconds.

(b) The student now stops moving her hand and the mass slowly comes to rest. How long after she stop shaking her hand will it take for the amplitude of the mass to reach one half its maximum amplitude?

I don't know how to start this.
 
Physics news on Phys.org
Do you know the equation of motion for the mass? If not, I'm pretty sure your physics textbook solves for it somewhere, so try looking for that.
 
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »
Thread 'A cylinder connected to a hanged mass'

Thread 'A cylinder connected to a hanged 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

Damped harmonic motion
Replies
3
Views
591
what the relation between the amplitude magnitude and mass at resonance?
Replies
5
Views
836
Distribution of Energy when work is done on a system of 2 masses connected by a spring
Replies
17
Views
1K
Difference between resonance in undamped vs damped mass-spring-dashpot
Replies
17
Views
2K
Question about springs and rotational/translational energy
Replies
4
Views
1K
Two spring-coupled masses in an electric field (one of the masses is charged)
Replies
1
Views
849
Simple harmonic motion -- The spring and mass are immersed in a fluid....
Replies
5
Views
2K
Distance traveled and period of a mass - spring - pulley system
Replies
13
Views
4K
Mass atop four springs with external input: Reduce vibration amplitude by factor of ten
Replies
3
Views
810
AQA physics paper On potential energy in mass spring system
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top