I have a problem with the method that they solved. This is what I mean ##\delta t= \frac{\pi L\alpha \delta T}{\sqrt{gL}}##. You can derive this equation by using errors and approximations here delta t is a tiny(not infinitesimal) change in time period, delta T is a tiny change in temperature...
TL;DR Summary: I was solving this problem given in a book. The answer I got was wrong and seems to violate the conservation of mechanical energy. Yet the forces were balanced. Can someone provide an explanation.
So here is the problem:
In the above arrangement, I had to find the time period...
So I proceed as:
Total time for 1 oscillation is 0.2s
$$\frac{1}{\sqrt{2}}=\sqrt{2} \sin ({\omega t_1})$$
$$\sqrt{2}=\sqrt{2} \sin ({\omega t_2})$$
Therefore
$$\omega t_2=\frac{\pi}{2}$$
$$\omega t_1=\frac{\pi}{6}$$
$$\omega ×2(t_1+t_2)=2×\left( \frac{\pi}{2}+\frac{\pi}{6}\right) $$
Since...
Same instruction was given while finding value of 'g' by a bar pendulum.
In the former case,does the spring obeys hooke's law while it forms a coupled harmonic oscillator system?Does the bar pendulum somehow breaks the simple harmonic motion(such that we can't apply the law for sumple harmonic...
The relevant equations has been me working out the gravitational potential energy. I was told to take the derivative twice from here, but I do not understand why. It leads into a taylor series expansion, which seems excessive, but I was not informed on any other way to do it. Any advice would be...
The speed of a wave in simple harmonic motion on a string is $$v= \sqrt{\frac{F}{\mu}}$$ where v= the horizontal velocity of the wave on a string.
Is the F the horizontal force or the resultant force (combination of Fy and Fx)?
The following attempt gives the wrong answer, and I would like to know where it goes wrong.
Let ##\theta## be the angle of the ball with the vertical passing through the centre of the bowl, and ##\phi## be the angle the ball rolls through.
Let ##m## be the mass of the ball, ##r## be the radius...
I first got the velocity of the combined mass with conservation of momentum and as it was in the mean position the velocity can be written as v = wA ( w= angular frequency , A = amplitude ) as we have to take it back to natural length i put A as the initial extension but i am getting a wrong ans...
I've got the answer for (a). It's k = 0.78 N/m.
I'm having problems with (b). I know that the equation of displacement in this case should either be :
x(t) = Asin(ωt + φ)
or
x(t) = Acos(ωt - φ)
where A = amplitudeFrom what I understand, both the equation above should give the same result as...
T = 2π * √(2/300), T = .513 seconds.
If I divide it by 4/3, I get a final answer of .385 seconds of touch.
I know the box isn't attached for the entire oscillation, so T has to be divided. To me, it makes sense to divide it by 4/3 (when the box falls, the spring is compressed, hits...
Homework Statement
Homework Equations
Kinetic Energy =1/2*m*v^2
Spring Potential Energy = 1/2*k*x^2
Gravitational Potential Energy = m*g*h
The Attempt at a Solution
I am thinking to solve this problem using energy conservation but I feel that it is not possible to apply energy conservation...
Description of the Problem:
Consider a spring-mass system with spring constant ##k## and mass ##m##. Suppose I apply a force ##F_0 \cos(\omega t)## on the mass, but the frequency ##\omega## is very small, so small that it takes the system, say, a million years to reach a maximum and to go to 0...
Homework Statement
A tuba is a instrument that can be modeled after a closed tube and has a length of 4.9m. A frequency of 122.5hz produces resonance in the Tuba. Is this the fundamental frequency of the instrument? If not, what harmonic is it?
Homework Equations
f=λv
4l=λ(open closed tube)
v=...
A mass attached to a spring is oscillating in Simple Harmonic Motion. If an other spring of same sprinc constant is attached parrallel to the other spring, what is the period of this new system (as a function of the initial period).
Here's what I did and have no idea if this is right:
For the...
Homework Statement A
A man applies a Force F on a spring block system shown.towards right when the block is at rest and spring is relaxed .If F is constant then
[/B]Homework Equations : F=-kx[/B]The Attempt at a Solution
The equilibrium position will be at the position where the disturbing...
Homework Statement :[/B]
Say for example I've got the equation of a SHM as: $$x = A \cos (\omega t + \phi)$$ where ##A## is the amplitude.
How do I find the time period of this motion?
Homework Equations :[/B]
Stated above.
The Attempt at a Solution :[/B]
I tried by finding the second...
Homework Statement
[/B]A heavy mass ##m## is suspended from two identical steel wires of length ##l##, radius ##r## and Young's modulus ##Y##, as shown in the figure above. When the mass is pulled down by a distance ##x## ##(x<<l)## and released, it undergoes...
I am very confused about angular velocity ω and why its used in simple harmonic motion. ω is described as θ/τ but when it comes to masses on springs, there is no angle - it is zero. Angular velocity comes from circular motion but the motion of SHM is not circular. My confusion is even greater...
While studying S.H.M., I found that the term ##\omega## is used quite a lot. The book says that this ##\omega## is the angular frequency.
What is this angular frequency? Why do we use ##\omega## rather than ##\nu##, that is, the normal frequency? All equations in S.H.M. are made with ##\omega##...
Homework Statement
Basically there is a results table for the time taken for 20 oscillations. Three examples are 9.90, 11.16 and 12.68. I need to work out the time period to the correct number of significant figures.
Homework EquationsThe Attempt at a Solution
I divide by 20 to get the time...
Homework Statement
[/B]Homework Equations
##F = -kx = m\ddot{x} ##
## f = \frac{2\pi}{\omega}##
## \omega = \sqrt{\frac{k}{m}} ##
##\ddot{x} + \gamma \dot{x}+\omega_o^2x = 0 ##
##\gamma = \frac{b}{m}##
The Attempt at a Solution
I'm stuck on part c of this question. Using the above equations I...
1. Homework Statement
Hey guys, I am reading my Physics book, in that specific section it says "the restoring force must be directly proportional to x or (because x=(theta)*L) to theta"
Homework Equations
The Attempt at a Solution
I have tried to look for that x=(theta)*L relationship...
1. Problem Description:
A massless spring hangs from the ceiling with a small object attached to its lower end. The object is initially held at rest at a position y. The object is then released from y and oscillates up and down, with its lowest position being 10cm below y.
What is the frequency...
Homework Statement
The drawing shows three situations in which a block is attached to a spring. The position labeled "0 m" represents the unstrained position of the spring. The block is moved from an initial position x0 to a final position xf, the magnitude of the displacement being denoted by...
Homework Statement
A spherical ball of mass “m”, moment of inertia “I” about any axis through its center, and radius “a”, rolls without slipping and without dissipation on a horizontal turntable (of radius “r”) describe the balls motion in terms of (x,y) for a function of time.
**The...
Hi all,
In short: For an air leg or air spring, there is a method using a Taylor approximation to find the spring constant for very small displacements, but I can't seem to figure out how it works. I've learned that air legs don't follow Hooke's law very much at all, except for when the...
Why is the rate of change of potential energy always same the rate of change of kinetic energy in a mass spring system?
Additiinally, How do we determine the rate of change of potential energy in such case?
Homework Statement
A mass "m" is attached to a spring of constant "k" and is observed to have an amplitude "A" speed of "v0" as it passes through the origin.
a) What is the angular frequency of the motion in terms of "A" and "v0"?
b) Suppose the system is adjusted so that the mass has speed...
Homework Statement
A 0.26-kg block on a horizontal frictionless surface is attached to an ideal massless spring whose spring constant is 190 N/m. The block is pulled from its equilibrium position at x = 0.00 m to a displacement x = +0.080 m and is released from rest. The block then executes...
Homework Statement
As in the given picture, the cylinder is drowned (not completely drowned as in partially drowned) in water. The cylinder is attached with a spring which has the spring constant of 200 N/m. The spring has attached to a unmovable point in the ceiling. The weight of the...
Homework Statement
A particle of mass 0.50 kg performs simple harmonic motion along the x-axis with amplitude 0.55m and period 4.3 seconds. The initial displacement of the particle is -0.30 m and it is traveling in the positive x-direction. The phase constant of the motion (Φ) = -2.15 rad...
Homework Statement
Homework Equations
None.
The Attempt at a Solution
Hi everyone. Apparently 5 is the right answer, although I chose D.
Could anyone please weigh in with their thoughts about why 5 is right and my answer is apparently wrong?
Thanks!