: A 50g mass vibrates in SHM at the end of a spring. The amplitude of the motion is 12cm
and the period is 0.1 minutes. Find the maximum speed of the mass. What will be the speed
atx= A/2?
Answers
Answer:
The motion of an object is said to be simple harmonic if the displacement from the mean position is directly proportional to the restoring force acting on the system.
Basic equations
The law of motion in one dimension is:
x
(
t
)
=
A
cos
(
ω
t
+
ϕ
)
, where
A
is the motion's amplitude,
ω
the angular frequency and
ϕ
the initial phase.
The velocity and acceleration as a function of time can be directly obtained computing the derivatives of the position
v
(
t
)
=
d
x
d
t
and
a
(
t
)
=
d
v
d
t
=
d
2
x
d
t
2
.
The amplitude and the initial phase are evaluated from the initial conditions
x
(
t
=
0
)
=
x
0
and
v
(
t
=
0
)
=
v
0
. Since the simple harmonic motion is described by a second-order differential equation two initial conditions are necessary.
Explanation:
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