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Problems Based on SHM with Spring Force ...
Problems Based on SHM with Spring Force - V
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Problems on SHM of Springs
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Problems on SHM of springs
2 mins
Important Questions
The frequency of vibration
′
f
′
of a mass
′
m
′
suspended from a spring of spring constant
K
is given by a relation of this type,
f
=
C
m
x
K
y
; where
C
is a dimensionless quantity. The value of
x
and
y
are
Medium
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>
Two masses
m
1
and
m
2
are suspended together by a massless spring of constant K as shown in figure. When the masses are in equilibrium,
m
1
is removed without disturbing the system. Find the angular frequency and amplitude of oscillation of
m
2
.
Medium
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>
A spring having with a spring constant 1200 N m
−
1
is mounted on a horizontal table as shown in the Figure. A mass of 3 kg is attached to the free end of the spring. The mass is then pulled sideways to a distance of 2.0 cm and released.
Determine (i) the frequency of oscillations, (ii) maximum acceleration of the mass, and (iii) the maximum speed of the mass.
Hard
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>
Two blocks
A
and
B
of masses
2
m
and
m
, respectively are connected by a massless and inextensible string. The whole system is syspended by a massless spring as shown in the figure. The magnitude of acceleration of
A
and
B
immediately after the string is cut, are respectively:
Medium
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>
A spring of force constant
K
is cut into two pieces such that the one piece is double the length of the other. Then the long piece will have a force constant of:
Medium
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>
Two masses of
1
k
g
and
2
k
g
respectively are connected by a massless spring as shown in figure. A force of
2
0
N
acts on the
2
k
g
mass. At the instant when the
1
k
g
mass has an acceleration of
1
0
m
s
−
2
towards right, the acceleration of the
2
k
g
mass is :
Hard
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>
Two identical springs of constant are connected in series and parallel as shown in figure. A mass
m
is suspended from them. The ratio of their frequencies of vertical oscillations will be
Medium
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>
A spring of spring constant 5 x
1
0
3
N/m is etched initially by 5 cm from the unstretched position the work required to stretch it further by another 5 cm is
Medium
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>
A spring balance has a scale that reads from
0
to
5
0
k
g
. The length of the scale is
2
0
c
m
. A body suspended from this balance, when displaced and released, oscillates with period of
0
.
6
s
. What is the weight of the body ?
Medium
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>
The time period of mass suspended from a spring is
T
. If the spring is cut into four equal parts and the same mass is suspended from one of the parts, then the new time period will be
Hard
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>