Theory of Machine
A simple spring-mass vibrating system has a natural frequency of fn. If the spring stiffness is halved and the mass is doubled, then the natural frequency will become

2 fn
4 fn
fn/2
8 fn

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Theory of Machine
A body is said to be under forced vibrations, when

None of these
There is a reduction in amplitude after every cycle of vibration
A body vibrates under the influence of external force
No external force acts on a body, after giving it an initial displacement

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Theory of Machine
Crowning on pulleys helps

In decreasing the slip of the belt
In increasing velocity ratio
For automatic adjustment of belt position so that belt runs centrally
Increase belt and pulley life

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