Physics - SHM Question with Solution | TestHub

If wedge moves towards left by x ,

deformation in spring is $\mathrm{y}=\mathrm{x}\sin \theta$ ⇒

spring force on wedge is ${\mathrm{F}}_1=\mathrm{kx}\sin \theta$

For wedge

$\left({\mathrm{k}}_1\mathrm{x}\sin \theta \right)\sin \theta ={\mathrm{ma}}_1$

${\mathrm{a}}_1=-\left(\frac{{\mathrm{k}}_1{\sin }^2\theta }{\mathrm{m}}\right)\times [-\mathrm{ve}\mathrm{sing}$ for restoring

nature]

comparing with $a_1=-{\omega }_1^{2}x\Rightarrow {\omega }_1=\sqrt{\frac{k_1{\sin }^2\theta }{M}}$

for deformation of right string ${\omega }_2=\sqrt{\frac{{\mathrm{K}}_2}{\mathrm{M}}}$

Time period of osc as $\mathrm{T}=\frac{\pi }{{\omega }_1}+\frac{\pi }{{\omega }_2}=\pi \sqrt{\frac{\mathrm{M}}{{\mathrm{k}}_1{\sin }^2\theta }}+\pi \sqrt{\frac{\mathrm{M}}{{\mathrm{k}}_2}}$