Unformatted text preview: EG-260 EGD260 Dynamics - Example Sheet 1 Single degree of freedom systems 1. Formulate the equation of motion for a simple pendulum of length l. If a grandfather clock requires the pendulum to have a period of 2 seconds, what is the required length? Compute the natural frequency and plot the solution of a spring- mass system & with m = 1kg and stiffness 4N/m given x0 = 1, x0 = 0 over 2 periods. An automobile is modelled as a 1000kg mass supported by a spring of 400000 N/m. When it oscillates it does so with a maximum deflection of 10cm. When loaded with passengers the mass increases to 1300kg. Calculate the change in natural frequency. Calculate the velocity amplitude and the acceleration amplitude if the maximum deflection remains 10cm. A machine oscillates in simple harmonic motion and appears to be well modelled by an undamped single degree of freedom oscillator. Its acceleration is measured to have an amplitude of 10 m/s2 at 8 Hz. What is the maximum displacement? 2 3 4 Answers
& g 1. & + = 0 l = 0.994m l 2. n = 2 rad s - 1 x (t ) = cos 2t 3. 1 = k k = 20 rads -1 2 = = 17.54 rads -1 m1 m1 -1 Change in frequency 2.46 rad s The velocity amplitude = 1.754 ms-1 The acceleration amplitude = 30.769 ms-2 4. A n = 10 ms -2 n = 2 f = 2 8 rad s -1 so 10 A = 2 = 0.00396 m = 0.396 cm n
2 @Avril Slone 2007 ...
View Full Document