- #1
Karol
- 1,380
- 22
Homework Statement
No friction. m3=5m, m2=12m, m1=3m
Prove that the system's acceleration when it's released is a=0.2g. is it the max acceleration?
Show that the equilibrium point is at x0=0.75L
Show that the kinetic energy of the system is E=mgL
Show that m2 will stop momentarily at ##x_1=\frac{15}{8}L##
Homework Equations
Harmonic motion, the force is proportional to the displacement: F=kx
$$\ddot x=\omega^2x=0$$
The Attempt at a Solution
The initial state:
$$\left\{ \begin{array}{l} m_1g-T=(m_1+m_2)a \\ T=m_2a \end{array}\right.\;\rightarrow a=\frac{3}{27}g=0.11g$$
It's wrong.
In the intermediate state:
$$l_1^2=x^2+\frac{L^2}{\sin^2\alpha}-2x \frac{L}{\sin\alpha}\cos\alpha$$
$$\Delta l=\frac{L}{\sin\alpha}-\sqrt{x^2-\frac{2L}{\tan\alpha}x+\frac{L^2}{\sin^2\alpha}}$$
$$\left\{ \begin{array}{l} m_1g-T_1=m_1\ddot x \\ T_1-T_3\cos\alpha=m_2\ddot\Delta l \\ T_3-m_3g=m_3\ddot\Delta l \end{array} \right.$$
It's complicated, Δl and it's derivative and i am afraid it won't get to a second order differential equation.