Define second's pendulum. Derive a formula for the length of second's pendulum. A particle performing linear S

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Q. Define second's pendulum. Derive a formula for the length of second's pendulum. A particle performing linear S.H.M. has maximum velocity 25 cm/s and maximum acceleration 100 cm/s². Find period of oscillations.

Maharashtra MsbshseMaharashtra HSC (MSBSHSE) Board 2022Subjective· 4mImportance★★★★★

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Second's pendulum length from T = 2π√(L/g) with T = 2 s; SHM period from ω = a_max/v_max, T = 2π/ω.

Second's pendulum: a simple pendulum whose time period is exactly 2 seconds, so that it completes one half-oscillation (one 'beat', or swing from one extreme to the other) in exactly 1 second.

Length: from $T = 2\pi\sqrt{L/g}$ , with $T=2$ s:

$L = \frac{gT^2}{4\pi^2} = \frac{(9.8)(4)}{4\pi^2} = \frac{39.2}{39.48} \approx 0.993\ \text{m}$

Numerical (SHM): $v_{max} = A\omega = 25$ cm/s, $a_{max} = A\omega^2 = 100$ cm/s². Dividing: …

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Q.Define second's pendulum. Derive a formula for the length of second's pendulum. A particle performing linear S.H.M. has maximum velocity 25 cm/s and maximum acceleration 100 cm/s². Find period of oscillations.

Concept understanding — Simple Pendulum

Q.Define second's pendulum. Derive a formula for the length of second's pendulum. A particle performing linear S.H.M. has maximum velocity 25 cm/s and maximum acceleration 100 cm/s². Find period of oscillations.

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