Find the magnitude and direction of the force acting on the particle of mass m during its motion in the plane xy according to the law x = a sin 
t, y = b cos 
t , where a, b and 
are constants.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
= – m ω 2 
, where 
is the radius vector of the particle relative to the origin of coordinates;
F = m ω 2 
]
Sol. 
or 
( a 2 = 0)
x = a sin ω t
v x = 
= aw cos ( ω t)
a x = 
= – a ω 2 sin( ω t)
v y = 
= – b ω sin( ω t)
a y = 
= – b ω 2 cos( ω t)
So, 
direction tan α = 
= 
cot( ω t) (from x-axis)
or 
is position vector of the particle in coordinate system. Because of negative sign
force is opposite to it and always acting towards the orzo.
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