A particle is oscillating in a straight line about a centre O, with a force directed towards O. When at a distance 'x' from O, the force is mn 2 x where 'm' is the mass and 'n' is a constant. The amplitude is a = 15 cm. When at a distance 
from O the particle receives a blow in the direction of motion which generates an extra velocity na. If the velocity is away from O at the time of blow and the new amplitude becomes 
cm, then find k.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(15)
K x 2 + 
mv 2 = 
KA 2
mn 2 x 2 + mv 2 = mn 2 a 2
v 2 = n 2 (a 2 – x 2 )
m (v + na) 2 + 
K 
= 
K A 1 2
m v 2 + 
mn 2 a 2 + 
mnav + 
mn 2 
= 
mn 2 A 1 2
mn 2 (a 2 – x 2 ) + mn 2 a 2 + 2mna n 
+ mn 2 
= mn 2 A 1 2
a 2 – x 2 + a 2 + 2a 
+ 
= A 1 2
11a 2 – 4x 2 + 8a 
= 4A 1 2 Putting x = 
a
12a
2 = 4A 1 2
A 1 = 
= 15 
cm
∴ k = 15
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