7.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{631b78c4-2763-4a1e-9d30-2f301fe3af2e-20_358_1161_278_452}
\captionsetup{labelformat=empty}
\caption{Figure 7}
\end{figure}
Two points \(A\) and \(B\) lie on a smooth horizontal table where \(A B = 41\).
A particle \(P\) of mass \(m\) is attached to one end of a light elastic spring of natural length I and modulus of elasticity 2 mg . The other end of the spring is attached to A . The particle P is also attached to one end of another light elastic spring of natural length I and modulus of elasticity mg . The other end of the spring is attached to B.
The particle \(P\) rests in equilibrium on the table at the point 0 , where \(A 0 = \frac { 5 } { 3 } I\), as shown in Figure 7.
The particle \(P\) is moved a distance \(\frac { 1 } { 2 } \mathrm { I }\) along the table, from 0 towards \(A\), and released from rest.
- Show that P moves with simple harmonic motion of period T , where
$$\mathrm { T } = 2 \pi \sqrt { \frac { l } { 3 g } }$$
- Find, in terms of I and g , the speed of P as it passes through 0 .
- Find, in terms of g , the maximum acceleration of P .
- Find the exact time, in terms of I and g , from the instant when P is released from rest to the instant when P is first moving with speed \(\frac { 3 } { 4 } \sqrt { g l }\)
\includegraphics[max width=\textwidth, alt={}, center]{631b78c4-2763-4a1e-9d30-2f301fe3af2e-20_2269_56_311_1978}
\(\_\_\_\_\) VIAV SIHI NI JIIHM ION OC
VILU SIHIL NI GLIUM ION OC
VEYV SIHI NI ELIUM ION OC