Question 5: By considering the expression x(z,t)=Ae"cos(bt+cz+d) what must the coefficients a, b, c and d be in order for the motion to be simple harmonic motion (SHM), damped harmonic motion (DHM) or travelling wave (TW)? (Here t is time, z is position, A is amplitude) a b SHM DHM TW
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- A thin 6-m string of mass 50.0 g is fixed at both ends and under a tension of 89 N. If it is set into small - amplitude oscillation, what is the frequency of the first harmonic mode?Then we have: A simple pendulum is made of a 2 m-string and a bob of mass m. At t = 0, the pendulum is at its equilibrium position and is given an initial velocity v = The maximum angular speed, O'max, is: 0.2 m/s. 0.1 rad/s 0.4 rad/s 0.05 rad/s 0.8 rad/s 0.2 rad/s A musical note on a piano has a frequency of 40 Hz. If the tension in the 2-m string is 308 N, and one-half wavelength occupies the string, what is the mass of wire?The midpoint of a guitar string demonstrates simple harmonic motion with motion following the form x(t) = A sin (wt +ϕ). It has an angular frequency of w = 2.65 x 103 s-1 and an amplitude of A=1.50 mm. The phase constant is ϕ= pi/2. What is the maximum magnitude of the acceleration of the string?
- Final Answer must be decimal or whole number only!!!The midpoint of a guitar string executes simple harmonic motion with motion following the form x(t) = A sin(wt + p). It has an angular frequency of w = 2.65 × 10³ s-¹ and an amplitude of A = 1.50 mm. Take the phase constant to be p = π/2.Problem 1: A simple harmonic oscillator is composed of a mass hanging from a spring. The mass of the hanging object is 400 g and the spring constant is 0.8 2. At the time t = 0 s, the mass is 2cm above its equilibrium position. The т amplitude of the oscillation is 5 cm. a) What is the initial phase? b) Find one of the times where the mass is located at 3cm above equilibrium. c) Find the kinetic and potential energies at t = 1s. d) What is the maximum kinetic energy?
- GggO At x = +0.025 m Consider a place where the gravity is one-ninth the gravity on Earth (g = g/9), then the frequency of oscillation of a simple pendulum in that place, f', as compared to its frequency on earth is: Of= 4f Of-f/2 f-f/3 O f- 2f O f-9f A musical note on a plano has a frequency of 31 Hz. if the tension in the 2-m The string what is the mass ofIC-3 A 167 gram mass is vibrating about its equilibrium position on the end of a spring as shown in problem SHM-8. While vibrating, the mass is observed to have a maximum speed of 0.500m/s and a maximum acceleration of 6.00m/s. At t0 the mass is at the equilibrium position with a velocity to the left. a) Find the numerical values for the angular frequency o and the amplitude of the motion xm. Hint: think about how Vm and xm are related. b) Find the value of the spring constant of the spring. c) The position of the block is described by x Xmcos(@t+0,). Find all possible values of 0, and then explain how to determine the value of 0, that corresponds to the given conditions. 99+ hp
- A simple pendulum consisting bf a point mass 'm' tied to a massless stringoflength 'l'executes small oscillations offiequency o and amplitude A= l Og. The average (over a compiete time period T= of the pendulum) tension on the string is |JNU 2013] ma?o? (b) (a) mg+ 4l (c) mg + 2l (d) 4lA particle oscillates according to x = Acos(ωt + δ) Determine the phase constant δ if the particle starts from x0 = −A.Suppose that you start procedure step 6 with an initial string-length, Li = 30 cm, and finish with a final length, Lf cm. In this process of going from Li to Lf , the linear frequency of the pendulum decreases such that we find: (fi − ff ) fi × 100 = 34, where fi is the frequency of the pendulum at Li and ff is its frequency at Lf . What is the value of Lf ?