At time t = 0, the displacement of a simple harmonic oscillator from the mean position is xo and the veloc- ity is vo. Obtain the expressions for the amplitude and phase constant of the oscillator in terms of x9, vo and w where w is the angular frequency of the oscillator.
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- plz answerThe figure below shows a piston from your car engine. Don't worry, you will not be required to understand an internal combustion engine for this problem. Instead, we simply notice that the up/down motion of the piston is exactly described as Simple Harmonic Motion. The tachometer on your dashboard tells you that your engine is turning at w = 1660 rpm (revolutions/minute). The owner's manual for your car tells you that the amplitude of the motion of the piston is Ymax = A = 0.099 meters. Simple Harmonic Motion wrist pin 500 grams Crankshaft A (top of stroke) B (midpoint) -C (bottom of stroke) y=-A y=+A Determine all the following: The angular frequency in proper units w = The period of the piston, T = The frequency of the piston, f = The maximum velocity of the piston, Vmax = meters/sec The piston velocity when y = 58% of full stroke, v(y = 0.58 Ymax) = seconds Hz rad/sec meters/secProblem 8 Show that the solution given for an underdamped harmonic oscillator, x(t) = Ae-bt/2m $), is a solution to the following differential equation cos(w't+ b dx k = 0. -r == dt2 т dt m k 62 Where w' = m 4m2
- A Simple Harmonic Oscillator has a displacement of x= (3.4 m) cos [(3.5 rad/s) t+ rad]. What is the %3D acceleration in m/s? at t= 9.8 s?A mass m = 3.2 kg is at the end of a horizontal spring of spring constant k = 310 N/m on a frictionless horizontal surface. The block is pulled, stretching the spring a distance A = 2.5 cm from equilibrium, and released from rest. 1: Write an equation for the angular frequency ω of the oscillation. 2: Calculate the angular frequency ω of the oscillation in rad/seconds. 3: Write an equation for the period T of the oscillations. 4: Calculate the period T of the oscillations in seconds. 5: Write an equation for the maximum speed vmax of the block. 6: Write an equation for the maximum acceleration amax of the block.We have a simple pendulum with a length of 5.2 m and a point mass of 3.3 kg at its end. Figure 1 shows the instant in which the sphere of the pendulum is at a height y = 0.15 m (measured from the lowest point reached by the mass following the arc of movement) and with a speed (v) of 0.20 m/s. Determine A. The mechanical energy of the oscillator. B. The maximum angle reached by the pendulum in radians. C. The maximum rapidity of the mass of the pendulum. D. If the initial speed were 0.20 m/s in the negative direction of movement, what changes would have to be considered for the previous parts? y = 0m 1 1 T n 1 1 1 1 00 1 B -y = 0,15 m
- For a simple harmonic oscillator with x=Asinωt write down an expression for the magnitude of acceleration. Please use "*" for products (e.g. B*A), "/" for ratios (e.g. B/A) and the usual "+" and "-" signs as appropriate (without the quotes).What is the smallest positive phase constant (ø) for the harmonic oscillator with the position function x(t) given in the figure below if the position function has the form x = Acos(ωt+ø)? The vertical axis scale is set by xs = 6.0 cm. Answer in radians. Hint: Evaluate at t=0 and solve for phi.An oscillator moves back and forth between the 10 cm and 50 cm marks on a meter stick. What is the location of the EP on the meter stick? In Problem 11, what is the amplitude A?
- In the figure provided, two boxes oscillate on a frictionless surface. The coefficient of static friction between the two boxes is 0.440 and the spring constant in the spring is 54.5 N/m. If the smaller box has a mass of 3.51 kg and the larger box has a mass of 8.47 kg, what is the maximum oscillation amplitude for which the 3.51 kg box does not slip?Quantum mechanics is used to describe the vibrational motion of molecules, but analysis using classical physics gives some useful insight. In a classical model the vibrational motion can be treated as SHM of the atoms connected by a spring. The two atoms in a diatomic molecule vibrate about their center of mass, but in the molecule HIHI, where one atom is much more massive than the other, we can treat the hydrogen atom as oscillating in SHM while the iodine atom remains at rest. A classical estimate of the vibrational frequency is ff = 7.0×10137.0×1013 HzHz. The mass of a hydrogen atom differs little from the mass of a proton. If the HIHI molecule is modeled as two atoms connected by a spring, what is the force constant of the spring? Express your answer to two significant figures and include the appropriate units. The vibrational energy of the molecule is measured to be about 5×10−20J5×10−20J. In the classical model, what is the maximum speed of the HH atom during its SHM?…For a simple harmonic oscillator with x=Asinωt write down an expression for the magnitude of acceleration.