S.H.M help?????

Question

a boy is oscillating in a swing in sitting position.
what happens to his frequency if he stands (and still oscillates) ?

Answer 1

Assuming all else stays the same, the only difference in the system is that the centre of mass has moved closer to the pivot. So, he will oscillate faster

Answer 2

Kinva.. is correct; sushant provides a good physical explanation.

When the girl stands up, she has to do work to lift her c.m.. The lifting force is pointing to the pivot (centre) so that the torque is zero and the angular momentum is conserved. The angular velocity increases because the moment of inertia is decreased. She will also swing at a larger amplitude because the new mechanical energy will increase as well. The addition of energy is provided by the work done.

In fact repeatedly squatting and standing is a common method for increasing the amplitude of the swing. One should time their pace of squarting/standing: squart when the swing is at the lowest height (fastest speed), and stand up when the swing is at the highest height (momentarily stationary). This will help efficiently transfer energy into the ocillation system. This open to the topic of forced oscillation. The driving frequency should be the same as the natural frequency in order for resonance to occur, and the phase of the driving force should be 90 deg out of phase with the natural oscillation.

Answer 3

In the above situation angular momentum will be conserved

If I is moment of inertia and V is angular velocity

=>I1V1=I2V2

The moment of inertia while standin will be less than when sitting (imagine a figure skater pulling hands inwards to increse speed).

=>v2
Since v is directly prpotional to f

=>f will decrease

Answer 4

formula for pendulum T=1/2L*(square root t/g)
as the length of the pendulum(i.e. the swing) remains the same. t(tension) will remain the same as event though the boy was in sitting position the swing still was carrying all his weight and g will remain the same I would think that his frequency will be the same

Answer 5

a=w^2 x R,
V=wxR,,,,,,,,,,,,w=omega is angular acceleration,w=2(pi)xf,,
There is not depending on the mass here.So that,hence it is
same.
.