1 of 2 Computer Applications, ME 325, 2016 Spring Computer Applications (ME 325)

Question

1 of 2 Computer Applications, ME 325, 2016 Spring Computer Applications (ME 325), Hw #6 Due date and time: 2/29,2:00 pm (before Class Time Note: PLEASE provide the KEY STEP(S) to reach your solution, otherwise zero credit wil be given. 1. (Differentiation) A figure shows a spring-mass system assuming the mass moves only horizontally, i. r-direction. The displacement of the mass (distance from the unstreched spring length) can be predicted by solving the second order differential equation, but here we simply postulate that the displacement of the mass can be modcled as xt0-coster) where x is the displacement [m], is the frequency [1 s], and ris the time [s]. We would like to study the displacement, and velocity of the mass for 0 SIS3 s. Note that eis(, but for the simple treatment we can use e-r. Use -0.1 s. The template of the excel sheet is shown below. (a) Calculate the velocity, ), of the mass using the analytie solution and MS-EXCEL at 0SIS3 s with every A (b) Calculate the velocity, v) of the mass using forward difference approximation (FDA) and MS EXCEL at 0

Explanation / Answer

t x = cos(pi*t) Analytic v(t) Numerical v(t) Forward Numerical v(t) Backward Numerical v(t) Central 0 1 0 -0.489434837 0.1 0.951056516 -0.970805519 -1.420395219 -0.489434837 -0.465480191 0.2 0.809016994 -1.84658183 -2.212317421 -1.420395219 -0.395961101 0.3 0.587785252 -2.541601846 -2.787682579 -2.212317421 -0.287682579 0.4 0.309016994 -2.987832165 -3.090169944 -2.787682579 -0.151243682 0.5 6.12574E-17 -3.141592654 -3.090169944 -3.090169944 -5.74627E-17 0.6 -0.309016994 -2.987832165 -2.787682579 -3.090169944 0.151243682 0.7 -0.587785252 -2.541601846 -2.212317421 -2.787682579 0.287682579 0.8 -0.809016994 -1.84658183 -1.420395219 -2.212317421 0.395961101 0.9 -0.951056516 -0.970805519 -0.489434837 -1.420395219 0.465480191 1 -1 -3.84892E-16 0.489434837 -0.489434837 0.489434837 1.1 -0.951056516 0.970805519 1.420395219 0.489434837 0.465480191 1.2 -0.809016994 1.84658183 2.212317421 1.420395219 0.395961101 1.3 -0.587785252 2.541601846 2.787682579 2.212317421 0.287682579 1.4 -0.309016994 2.987832165 3.090169944 2.787682579 0.151243682 1.5 -1.83772E-16 3.141592654 3.090169944 3.090169944 1.72388E-16 1.6 0.309016994 2.987832165 2.787682579 3.090169944 -0.151243682 1.7 0.587785252 2.541601846 2.212317421 2.787682579 -0.287682579 1.8 0.809016994 1.84658183 1.420395219 2.212317421 -0.395961101 1.9 0.951056516 0.970805519 0.489434837 1.420395219 -0.465480191 2 1 7.69783E-16 -0.489434837 0.489434837 -0.489434837 2.1 0.951056516 -0.970805519 -1.420395219 -0.489434837 -0.465480191 2.2 0.809016994 -1.84658183 -2.212317421 -1.420395219 -0.395961101 2.3 0.587785252 -2.541601846 -2.787682579 -2.212317421 -0.287682579 2.4 0.309016994 -2.987832165 -3.090169944 -2.787682579 -0.151243682 2.5 -1.47007E-15 -3.141592654 -3.090169944 -3.090169944 4.98625E-15 2.6 -0.309016994 -2.987832165 -2.787682579 -3.090169944 0.151243682 2.7 -0.587785252 -2.541601846 -2.212317421 -2.787682579 0.287682579 2.8 -0.809016994 -1.84658183 -1.420395219 -2.212317421 0.395961101 2.9 -0.951056516 -0.970805519 -0.489434837 -1.420395219 0.465480191 3 -1 -1.15468E-15 -0.489434837

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