(1) Why is external force sinusoidal? Since there is no phase shift, I assume the omega in the external force's cosine is same as the omega of the harmonic system? Otherwise the system would not be "simple" (2) Why is friction modeled as a function of velocity? I thought { dynamic-friction = coefficient*normal-force } and friction is a function of mass...
Friction takes away the momentum of an object so the velocity is negative because there is no such thing as a negative mass (that we know about). The external force changes the period and frequency of the fundamental oscillation and therefore can be modeled by a consine wave. It’s cosine because at t = 0 the force is maximized and tapers off until it matches the normal mode at multiples of 2pi.
Hello and thank you sir for your really great educational lessons I have question please : When you write F=ma , are you projecting the forces along the +ve axis? , because in this case we might have two different differential equations if we assume the acceleration is in the direction of the -ve x-axis ?? , or are you writing F=ma in the general vector forms without projretion on any x-axis direction? Thank you in advance
@@ProfJeffreyChasnov Thank you for your reply Yes , but with one dimension it can be either positive or negative What i meant in my question is that you assumed that acceleration is in the positive x direction , but during oscillation when the acceleration is in the negative x direction we will have diffent differential equation with a minus sign to (ma) ?? , whats wrong with this analysis ?? Thank you
Can you explain what exactly c is in this video? I'm having trouble seeing how c*dx/dt equals a force as inserting simply the frictional constant results in a velocity, but also when inserting c as the frictional force it results in a power.
@@emilkiholm931 The assumption is that the frictional force is proportional to the velocity of the mass. The constant c is just the proportionality constant. We know that if the mass is at rest, the frictional force should be zero, so it is in someway a linear approximation for this force.
@@ProfJeffreyChasnov I love your series and it has helped me alot! But this seems really weird to me. Assuming we're talking about dry friction, the frictional force is just a constant in the opposite direction of movement and not linearily dependent on velocity. But for sure we can assume this in math world. Also assuming F_e is pushing to the left, shoudlnt it be -F_0 coswt for the ode?
@@ProfJeffreyChasnov could you just give the final equation like one with a second-order differential equation? I am confused, what to after putting down mg into the system.
Hi, here the springs are working on a plane perpendicular to the ground, so gravity fundamentally does not act on the box since gravity pushes on the y-direction (towards the center of the Earth)
Find other Differential Equations videos in my playlist th-cam.com/play/PLkZjai-2JcxlvaV9EUgtHj1KV7THMPw1w.html
as a social science student who just jumped to mathematics and physics fields, this is so easy to understand. thank you, you deserve more viewers!
These videos are awfully well made. Thanks Jeffrey Chasnov!
F=uN getting thrown out the window is an accurate representation
You are better at writing reversed than I am at writing normally ... :)
They have flipped the video
the video is flipped there are mirrors present there
.... is no one gonna mention how he is probably writing in mirrored? or was it mirrored in post production? prob the latter
(1) Why is external force sinusoidal? Since there is no phase shift, I assume the omega in the external force's cosine is same as the omega of the harmonic system? Otherwise the system would not be "simple"
(2) Why is friction modeled as a function of velocity? I thought { dynamic-friction = coefficient*normal-force } and friction is a function of mass...
Friction takes away the momentum of an object so the velocity is negative because there is no such thing as a negative mass (that we know about). The external force changes the period and frequency of the fundamental oscillation and therefore can be modeled by a consine wave. It’s cosine because at t = 0 the force is maximized and tapers off until it matches the normal mode at multiples of 2pi.
This is very helpful. I also couldn’t help but notice you looks like a young Jonathan banks.
Very good lecture Sir. Thanks and Regards 🙏🙏🙏😊😊
Hello and thank you sir for your really great educational lessons
I have question please :
When you write F=ma , are you projecting the forces along the +ve axis? , because in this case we might have two different differential equations if we assume the acceleration is in the direction of the -ve x-axis ?? , or are you writing F=ma in the general vector forms without projretion on any x-axis direction?
Thank you in advance
I am treating a one-dimensional problem
@@ProfJeffreyChasnov
Thank you for your reply
Yes , but with one dimension it can be either positive or negative
What i meant in my question is that you assumed that acceleration is in the positive x direction , but during oscillation when the acceleration is in the negative x direction we will have diffent differential equation with a minus sign to (ma) ?? , whats wrong with this analysis ??
Thank you
Can you explain what exactly c is in this video? I'm having trouble seeing how c*dx/dt equals a force as inserting simply the frictional constant results in a velocity, but also when inserting c as the frictional force it results in a power.
Or more direct: can you solve for the value of c, if you know the frictional constant and mass?
@@emilkiholm931 The assumption is that the frictional force is proportional to the velocity of the mass. The constant c is just the proportionality constant. We know that if the mass is at rest, the frictional force should be zero, so it is in someway a linear approximation for this force.
@@ProfJeffreyChasnov I love your series and it has helped me alot! But this seems really weird to me. Assuming we're talking about dry friction, the frictional force is just a constant in the opposite direction of movement and not linearily dependent on velocity. But for sure we can assume this in math world. Also assuming F_e is pushing to the left, shoudlnt it be -F_0 coswt for the ode?
This video is good. Thank you sir
These are well made, thank you :)
can you show gravity as a disturbance of the system? what would be the differential equation?
You can add forces and use Newton's law to write the differential equation.
@@ProfJeffreyChasnov could you just give the final equation like one with a second-order differential equation? I am confused, what to after putting down mg into the system.
Hi, here the springs are working on a plane perpendicular to the ground, so gravity fundamentally does not act on the box since gravity pushes on the y-direction (towards the center of the Earth)
Great explanation :)
F=-c * dx/dt....what is C?
Thank sir
sorry but you don't explain very well why things are like they are