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.b)find analytic expressions for the arbitrary constants a and ϕ in equation 1 (found in part a) in terms of the constants c and s in equation 2 (found in part b), which are now considered as given parameters. express the amplitude a and phase ϕ (separated by a comma) in terms of c and s.

Which of the following represents an upside-down image?

For problems 1-3, consider a simple dc brush motor with a permanent magnet stator. with an an consider a simple dc brush motor with a permanent magnet ae supply voltage of 100 v, the no-load speed of the motor is 1000 rpm. this motor can provide a torque of 1.9 n-m at 800 rpm drawing a current of 2 a current are both zero at no load.) 1. with an armature supply voltage of 100 v, the motor is operated at 900 rpm. what is the motor torque? what is the mechanical power delivered by the motor? what is the current draw? what is the electrical power input? what is the energy efficiency of the motor? with an armature supply voltage of 100 v, the motor is operated at 1100 rpm (where it acts as a generator). what torque input is required? what mechanical power is required what current is generated? what is the electrical power generated? what is the energy efficiency of the motor acting as a generator? 2. with an armature supply voltage raised to 120 v, the motor is operated at 1000 rpm. what is the no-load speed? what is the motor torque? what is the mechanical power delivered by the motor? what is the current draw? what is the electrical power input what is the energy efficiency of the motor? 3.

An airplane is flying with a velocity of 240 m/s at an angle of 30.0∘ with the horizontal, as the drawing shows. when the altitude of the plane is 2.4km,a flare is released from the plane. the flare hits the target on the ground. what is the angle θ?