Question

Parameter Variable Units Amplitude A m MAS kg Spring A constant N/m External Force F N Frequency rads

A system made up of a mass (m) attached to a spring (k) will oscillate to a specific amplitude (a) depending on an external force (f) and initial conditions. If all the variables involved are given in the table, formulate the necessary Pi groups to describe this behavior.

Answer 1

please provide upvote and support my efforts..!

Let us write these variables with their dimensions the question are mass, spring constant, external force, frequency given variables from Ampettuce, as following Amplitude an [LT]. M (M27]. External force F→ [MET. Spring Constant ky [M2052]. frequency, on [m2ott] , Total of variables = 5an. Number of fundamental variables=32m. No of pitems used will be. (nom)-5-322. & from the above line we can conclude Pig Pe are two required Pi-term which are dimenionless, - The no. of repeating terms will be ma3. A m, w. we have As [m LT"]. LaA 0. Similarly find for the remaining. [mety Mon - (MLT) = = Taus which are we Can wa

mol we have ka [m27-2] kx[m2 +2] will be dimenionless ... PEK [[m') CAJ°C w }]. " Piek is one pi-term . Pi=k moz, we celso have, f [mLT. Fx [mit't?] will be dimensionless, :P2=F[[m] CAJW)?] . i P2 Z F ů another pirterm. mawa by solving the requiral Pin groups we got PizK and P22 F mo 1P2= f(PD) - The celove is fixed and the problem can be Sloved the steps listed above, go through have any doubts. ques هنر MAWR by once if you - thanking your *please provide up-vole and support my effort*