Question 14: Oscillations

Question

Two spring of force constant $$k_1$$ and $$k_2$$ are configured as the figure given below
The angular frequency of this configuration is

Accepted Answer

The equation of motion of this system about mean position is given by
$$F = {k_1}x + {k_2}x$$
$$ \Rightarrow m{{{d^2}x} \over {d{t^2}}} = {k_1}x + {k_2}x \Rightarrow {{{d^2}x} \over {d{t^2}}} = x\left( {{{{k_1} + {k_2}} \over m}} ight)$$
$$\because$$ $$a = {{{d^2}x} \over {d{t^2}}} = {\omega ^2}x$$
$$	herefore$$ $${\omega ^2} = {{{k_1} + {k_2}} \over m}$$ or $$\omega  = \sqrt {{{{k_1} + {k_2}} \over m}} $$

Answer

$${{{k_1} + {k_2}} \over m}$$

Answer

$$\sqrt {{{{k_1} + {k_2}} \over m}} $$

Answer

$$\sqrt {{{{k_1}} \over {{k_2}m}}} $$

Answer

$${{{k_2}m} \over {{k_1}}}$$

Oscillations

Two spring of force constant $k_1 and k_2$ are configured as the figure given below The angular frequency of this configuration is

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