The frequency of oscillation of a compound pendulum is

A 1/2π √g.h/k2G +h2
B 1/2π √k2G +h2/g.h
C 2π√g.h/k2G +h2
D 2π√k2G +h2/g.h

Correct Answer: 1/2π √g.h/k2G +h2

We know that the periodic time, tp = 2π√Displacement/Accleration = 2π√θ/α and frequency of oscillation,n = 1/tp = 1/2π √g.h/k2G +h2 where kG = Radius of gyration about the centroidal axis, and h = Distance between the point of suspension and centre of gravity of the body.
Bissoy MCQ
#Machine Kinematics #Simple Harmonic Motion

Related Questions

The periodic time of one oscillation for a simple pendulum is (where $$l$$ = Length of the pendulum.)
A $$\frac{1}{{2\pi }}\sqrt {\frac{l}{{\text{g}}}} $$
B $$\frac{1}{{2\pi }}\sqrt {\frac{{\text{g}}}{l}} $$
C $$2\pi \sqrt {\frac{l}{{\text{g}}}} $$
D None of these
The equivalent length of a simple pendulum which gives the same frequency as compound pendulum is
A $$\frac{{\text{h}}}{{{\text{k}}_{\text{G}}^2 + {{\text{h}}^2}}}$$
B $$\frac{{{\text{k}}_{\text{G}}^2 + {{\text{h}}^2}}}{{\text{h}}}$$
C $$\frac{{{{\text{h}}^2}}}{{{\text{k}}_{\text{G}}^2 + {{\text{h}}^2}}}$$
D $$\frac{{{\text{k}}_{\text{G}}^2 + {{\text{h}}^2}}}{{{{\text{h}}^2}}}$$
The length of a simple pendulum which gives the same frequency as the compound pendulum, is
A $${\text{kG}} + {l_1}$$
B $${\text{k}}{{\text{G}}^2} + {l_1}$$
C $$\frac{{{\text{k}}{{\text{G}}^2} + l_1^2}}{{{l_1}}}$$
D $$\frac{{{\text{kG}} + l_1^2}}{{{l_1}}}$$
The equivalent length of a simple pendulum which gives the same frequency as a compound pendulum is
A $$\frac{{\text{h}}}{{{\text{k}}_{\text{G}}^2 + {{\text{h}}^2}}}$$
B $$\frac{{{\text{k}}_{\text{G}}^2 + {{\text{h}}^2}}}{{\text{h}}}$$
C $$\frac{{{{\text{h}}^2}}}{{{\text{k}}_{\text{G}}^2 + {{\text{h}}^2}}}$$
D $$\frac{{{\text{k}}_{\text{G}}^2 + {{\text{h}}^2}}}{{{{\text{h}}^2}}}$$
If the radius of gyration of a compound pendulum about an axis through e.g. is more, then its frequency of oscillation will be
A Less
B More
C Same
D Data are insufficient to determine same
The frequency of oscillation of a torsional pendulum is
A 2πkG/r √g/I
B r/2πkG√g/I
C 2πkG/r√I/g
D r/2πkG√I/g
It is observed that in a certain sinusoidal oscillation, the amplitude is linearly dependent on the frequency f. If the maximum velocity during the oscillation is V, then V must be proportional to
A f
B $$\frac{1}{{\text{f}}}$$
C $$\frac{1}{{{{\text{f}}^2}}}$$
D f2
To double the period of oscillation of a simple pendulum
A The mass of its bob should be doubled
B The mass of its bob should be quadrupled
C Its length should be quadrupled
D Its length should be doubled
The periodic time of one oscillation for a simple pendulum is
A $$2\pi \sqrt {\frac{{\text{g}}}{l}} $$
B $$\frac{1}{{2\pi }}\sqrt {\frac{{\text{g}}}{l}} $$
C $$2\pi \sqrt {\frac{l}{{\text{g}}}} $$
D $$\frac{1}{{2\pi }}\sqrt {\frac{l}{{\text{g}}}} $$
For a simple pendulum, the period of one oscillation is
A $$2\pi \sqrt {\frac{l}{{2{\text{g}}}}} $$
B $$2\pi \sqrt {\frac{{2{\text{g}}}}{l}} $$
C $$2\pi \sqrt {\frac{l}{{\text{g}}}} $$
D $$2\pi \sqrt {\frac{{\text{g}}}{{2l}}} $$

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