Ex. 44: The equation of linear S.H.M. is (1) 6 x = 10 sin 4t+ cm. Write down the values of amplitude, period and phase constant. Also 1 find phase angle second after the start. 24
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- A 250 g mass on a 28 spring is initially displaced +.02 m from the equi- librium position and has an initial velocity of -.25 m. 1. Determine the amplitude of the motion. 2. Determine the phase angle of the motion. 3. Write equations for the position x(t) and velocity v(t) of the mass.Problem 5 02 k m m Two identical pendulums, each with mass m and length I, are connected by a spring of stiffness k at a distance d from the fixed end, as shown in the above Figure a. Derive the equations of motion of the two masses. b. Find the natural frequencies and mode shapes of the system. Answer Given DataFor a simple harmonic oscillator with x = A sin ot write down an expression for the velocity. Please use "*" for products (e.g. B*A), "/" for ratios (e.g. B/A) and the usual "+" and "-" signs as appropriate (without the quotes). For trigonometric functions use the usual sin and cos, while for Greek letters such as w, use omega. Please use the "Display response" button to check you entered the answer you expect. U= Display response
- You may also recall that for a simple pendulum N = V, where g is the acceleration due to gravity and L is the length of the pendulum. This has been inserted in Equation 4 above. Lastly, this means that angular position 0 of the pendulum is given by: 0 = 0, cos(Nt) Equation 5 Question 1 Use the information above and Equation 2 to write an equation for the period of the pendulum in terms of g and L.Ex 1. Get the motion equations for the double pendulum shown in the Fig.14 for when unknowns are X1 and X2. Consider that the system suffers small angular variations. Calculate the natural frequencies and vibrate modes. Given m1 = m2 = m and L1 = L2 = L: s u un L m2 Fig. 14: Illustration of the double pendulum Ex 2. Considering the previous exercise, derive the equations of movement using coordinated 0, and 02. Next, get the natural frequencies and ways to vibrate.Please help thank you