Problem. Consider a violin string of length L = 20 cm with fixed ends at x = 0 andx = L.(a) Find the particular solution u(x, t) given that at t = 0 the string was ‘plucked’in the middle and released, tha t is:u(x, 0) =Dx for 0 ≤ x < L/2D(L − x) for L/2 ≤ x < L, (6)with D = 0.5 cm.1 (b) Find the frequency of the ‘fundamental no te’, ν1= ω1/(2π) assuming a velocityc = 500 m/s.(c) The ‘power’ of the sound at a particular radian frequency ωnis given by thesquared magnitude of the amplitude of the wave-component bnat that frequency, that is P (ωn) = |bn|2. Find the ratio between the power of the first harmonic(that is, at radian frequency ω2) and of the fundamental at f requency ω1. Thatis, find | b2/b1|2. This will show how the power of the higher harmonics decreasesas the frequency increases.(d) Does the ratio |b2/b1|2depend on the amplitude D of the initial displacement(that is, on how hard we pluck the string)?

If forces acting on an object are unbalanced, which factors may result fron an unbalanced force? check all that apply

Consider a system with two masses that are moving away from each other. why will the kinetic energy differ if the frame of reference is a stationary observer or one of the masses?

To understand the behavior of the electric field at the surface of a conductor, and its relationship to surface charge on the conductor. a conductor is placed in an external electrostatic field. the external field is uniform before the conductor is placed within it. the conductor is completely isolated from any source of current or charge. part a: which of the following describes the electric field inside this conductor? it is in the same direction as the original external field. it is in the opposite direction from that of the original external field. it has a direction determined entirely by the charge on its surface. it is always zero. part b: the charge density inside the conductor is: 0non-zero; but uniformnon-zero; non-uniforminfinite part c: assume that at some point just outside the surface of the conductor, the electric field has magnitude e and is directed toward the surface of the conductor. what is the charge density η on the surface of the conductor at that point? express your answer in terms of e and ϵ0