The net force also includes the force of gravity on the mass, and not only the restoring force; this was missing. To make this equation still work, you could make the mass oscillate horizontally on a frictionless surface: now the net force would equal to the restoring force.
the potential energy due to gravity goes to zero when kinetic energy is 0, at A, so the restoring force is just the spring. Gravity doesn't effect this oscillation it. just like a horizontal spring on a mass
He should work more on his style. Good content, not very good style of presentation; He needs a more calm approach; He seems to be shouting at the student. Greatly thankful for the effort and content, nevertheless.
AK LECTURES Hello Kyle: You have some of the awesome lectures. Instead of going through all the really complex equations, you make it very very simple for everyone to understand. Way to go !!
Take the equation of motion of SHO and subtract kx to both sides and then divide both sides by -k. You get that some constant (-m/k) times the second derivative of x with respect to time is equal to x itself. In other words; we are looking for a function that after you take the second derivative you get the same function with what you started with (times a constant). Well this property is fullfiled by cos(x) and sin(x). For example. We have x(t) = cos(w*t), where w is a constant. First derivative: -w*sin(w*t). Second derivative: -w^2cos(w*t). We get that the second derivative is a constant times the function x(t) we started with and this is why cos(x) solves the equation. So you basically guess by knowing that the second derivative of cosine (and sine) is itself times something...
I salute you sir,,,, your content is quite comprehensive🤛🤛🤛
Just a beautiful explanation
The net force also includes the force of gravity on the mass, and not only the restoring force; this was missing. To make this equation still work, you could make the mass oscillate horizontally on a frictionless surface: now the net force would equal to the restoring force.
the potential energy due to gravity goes to zero when kinetic energy is 0, at A, so the restoring force is just the spring. Gravity doesn't effect this oscillation it. just like a horizontal spring on a mass
Wont we consider Gravitational for in sum of forces?
wonderful bro wonderful..
why didn't you consider the effect of "g"in the calculation of time period????
Very very neat.
why not, mg- kx= ma???
great work
Thank you!
He should work more on his style. Good content, not very good style of presentation; He needs a more calm approach; He seems to be shouting at the student.
Greatly thankful for the effort and content, nevertheless.
i need its compelet solution of equation of motion, i did'nt find other lectrus about this topic
#HELP... sir how do i know if a given equation is a SHM or just a periodic motion?????
pls help
Check whether the given equation is in the form of y = Asin(wt ± ∅),if yes its SHM. (somebody,do correct me,if i am wrong)
Nice work!!!
Thanks Kyle!
AK LECTURES Hello Kyle: You have some of the awesome lectures. Instead of going through all the really complex equations, you make it very very simple for everyone to understand. Way to go !!
Naresh Mantravadi Thats great to hear! By the way, my name is Andrey, not Kyle! I think you have me confused with the above commenter :D
😍interesting
thank u sir
this is substitution, how can we do derivation?
Why guess position is in cosine terms
Take the equation of motion of SHO and subtract kx to both sides and then divide both sides by -k. You get that some constant (-m/k) times the second derivative of x with respect to time is equal to x itself. In other words; we are looking for a function that after you take the second derivative you get the same function with what you started with (times a constant). Well this property is fullfiled by cos(x) and sin(x). For example. We have x(t) = cos(w*t), where w is a constant. First derivative: -w*sin(w*t). Second derivative: -w^2cos(w*t). We get that the second derivative is a constant times the function x(t) we started with and this is why cos(x) solves the equation. So you basically guess by knowing that the second derivative of cosine (and sine) is itself times something...
@@estebanvprado nice answer
But sir x= Asin(wt + constant ) ? I am confused .
Both work. Acos(wt+phi) is just pi/2 translated to the left. The phi phase angle adjusts for the starting angle (set t=0).