To understand how the two standard ways to write the general solution to a harmonic oscillator are related. there are two common forms for the general solution for the position of a harmonic oscillator as a function of time t: x(t)=acos(ωt+ϕ) andx(t)=ccos(ωt)+ssin(ωt).either of these equations is a general solution of a second-order differential equation (f⃗ =ma⃗ ); hence both must have at least two--arbitrary constants--parameters that can be adjusted to fit the solution to the particular motion at hand. (some texts refer to these arbitrary constants as boundary values.)a)find analytic expressions for the arbitrary constants c and s in equation 2 (found in part b) in terms of the constants a and ϕ in equation 1 (found in part a), which are now considered as given parameters. give your answers for the coefficients of cos(ωt) and sin(ωt), separated by a comma. express your answers in terms of a and ϕ.

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

true tan speed = ang vel x radius

c)   sound waves travel through solids like the string.

it is a is not the