21. A 4kg mass is attached to a spring of spring constant 400 Nm". It is made to vibrate on a frictionless rod. The mass is displaced through a distance of 10 cm from the equilibrium position and then released. Calculate (a) the time period of oscillation (b) the maximum speed of vibratlon (c) the maximum acceleration of the attached mass. 1+1+1-3
Answers
Answered by
1
By energy conservation, we have,
2
1
mv
max
2
=
2
1
kx
2
2
1
×4×v
max
2
=
2
1
×100×(
10
1
)
2
v
max
=0.5 m/s
Answered by
0
Answer:
(a) 0.2 π (b) 1 m/s (c) -10 m/s²
Explanation:
Given: mass ,m =4kg
spring constant,k=400N/m
mass is displaced,x = 10 cm= 1/10m
(a) we know,
T=2π√m/k
=2π √(4/400)
=2π (1/10)
=0.2π
(b) by conservation of energy
1/2 m v² = 1/2 k x²
mv²=kx²
4 v²=400 (1/10)²
v² = 400/(4 x 100)
v = 1 m/s
(c) we know
F=ma
F=-kx
ma=-kx
4 a = - 400 (1/10)
a = -400/40
a=- 10m/s²
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