Question

A block of mass m is attached by means of a spring of constant to a wedge of mass and height that forms an angle $\alpha$ with the horizontal, as shown in the figure. Mass can slide on the horizontal surface. Note: don't consider friction.
a) Calculate the frequencies of small oscillations of the system around equilibrium.
b) Find and schematically draw the relative configurations of the normal modes corresponding to each frequency of the system.

Answer 1

T mg Sina - Kx = ma-m?acou zot CM+m) => mg sinak ma (Mtm)-m²a cosad (Mm) => mg sina - -kx = Mma tm²a sind (Mim) mg sinar-Ka = ma CM+m Sinood) (M+m) s ma (M+m Sinia) + kac CM+m) -masing = at Koc masina mo(M+ m Sinn) CM+m) m (Mumsin?a) Mim Constant at CMim) Ku mCM+msina) it with constant, Comparing equation cation d²x + o2x = dt² we get w= (Mt mit m (M+msin) CS Scanned with CamScanner

(6) Therefore, Dięplacement me A cos (wt+) Where will of blow nim CS Scanned with CamScanner