Wave equation with damping & forcing: derivation for a string

Using Newton's second law to derive the wave equation for a string undergoing small transverse displacements, including the effects of damping and external forces. We'll consider how to solve the resulting partial differential equation in future videos!

About me: I studied Physics at the University of Cambridge, then stayed on to get a PhD in Astronomy. During my PhD, I also spent four years teaching Physics undergraduates at the university. Now, I'm working as a private tutor, teaching Physics & Maths up to A Level standard.

#physics #waves #differentialequation #partialdifferentialequation #partialderivatives #newtonslaws #damping #dissipation #string #tension #calculus #mathematics #maths #math #science #education

[postsilike]

Hello dear, what about if we want to include the impact of thermal stress ?

[mokshsurya]

Sir where to find other video where you apply this equation. Just cuosity leads to a class 12 student to see most general equation for us (damping, forced ossilation combined) and it turn oit to be intresting😅😅.

[mokshsurya]

Sir, why we take angle of upper T acting on length element as theta+d(theta) not theta - d(theta) as upper angle is less then lower angle(angle made by lower T with horizontal?

[fatherland]

for the force equation in y direction you wrote rho * dx * y'' = (F * dx - b * y' * dx)+ T * d(theta) but the units are inconsistent here. On the right side you are adding Newton * meter + Newton.