In Problems 6 and 7, use a trigonometry formula to write the two terms as a single harmonic. Find the period and amplitude. Compare computer plots of your result and the given problem. 6. sin 2r + sin 2(r+/3) 7. COS TL = COS T(T – 1/2)
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- Need help with part A and B and C pls. Part C asks: If the angular displacement can be written as θ=Ae^(−γt)cosω′t, find how long it takes for the amplitude to be reduced to 1/2 of its original value.Explain the term amplitude as it relates to the graph of asinusoidal function.Consider a thin hoop of mass (1.420 ± 0.001) kg and radius (0.250 ± 0.002) m. The moment of inertia for a thin hoop rotating about an axis going through its center is MR2 . Calculate the moment of inertia of this hoop and its uncertainty using error propagation rules (see Appendix). Clearly show work. Please solve the uncertainty using the appendix I attached
- This is the equation for a math related physics problem Let’s assume that the period T depends on the length L in a non-linear way, namely a power law: T=aL^b - Take the logarithm of both sides, and reduce this equation by using the rules for logarithms: In your final reduction, you should recognize that some values are constant, while one term is dependent upon the length L (specifically on log10(L)) You plot data to make a plot of log10(L) vs log10(T) (L is independent axis). - Answer: what is the reduced equation? What is the mathematical relationship between the slope of the log-log line and the unknowns a and b? What is the mathematical relationship between the intercept of the log-log line with the vertical axis and the unknowns a and b?Please solve only: (c). the amplitude of the motion.For each of the following functions, identify the amplitude, period, and horizontal shiftand then use this information to sketch one complete cycle of the graph. y = sin ( x+ pi/4)
- The period of a clock pendulum T is given by the equation T = 2π√Lg where the constant L is thelength of the pendulum and g is the acceleration due to gravity. The period of the clock pendulumvaries slightly depending on where it is located on earth’s surface, due to small changes in g.(a) If g increases, will T increase or decrease? Does this correspond to the clock speeding up orslowing down? Explain your reasoning.(b) Find the linear approximation for T (g) centered at g = 980 cm/sec2, if the length of the pendulumis 400 cm.(c) When a clock with a 400 cm pendulum is moved from a location where g = 980 cm/sec2to anew location, its period increases by .001 sec. Estimate the amount by which g changes andapproximate the value of g at the new location.An electron undergoes simple harmonic motion with the acceleration shown below: ax(t)=−amaxsin(2t/T) with amax=5839 ms2 and T=316 seconds. Assuming that the only motion is oscillatory (ignoring overall translation), what is the maximum speed of the electron? What is the amplitude of the electron's position?Given the acceleration as a function of the angle theta, a =6.5sinθ + 2.3cosθ. Find the optimal angle, so the acceleration is maximum Find the value of the maximum acceleration I have found the derivative of the function but am confusing myself on the next steps.
- To be able to solve rectilinear problems with variable functions. A particle moves with harmonic motion over a path 10in long in 10sec. Find A, V and t when it has moved 5in from one end.Write the equations that describe the simple harmonic motion of a particle moving uniformly around a circle of radius8units, with linear speed 3units per second.How do you find the finding the theta for the components of Ab? the equations I have found to solve the problem is... Ay-FABSin(theta)=0 and -FABCos(theta)+Ax-FAG=0 because Ay is shown in tension and Fab and FAG Is assumed to be in compression. round your answers to three decimal places and state if the member is in compression or tension (if the number you find for a member negative the the direction we assumed is wrong)