Phys101
Term:121
Online HW-Ch15-Lec01
Q1:
A particle moves back and forth along the x axis from x = +x m to x = -x m , in simple
harmonic motion with period T. At time t = 0 it is at x = +x m . When t = 0.75T:
A.
B.
C.
D.
E.
it is at x = 0 and is traveling toward x = -x m
it is at x = 0 and is traveling toward x = +x m
it at x = +x m and is at rest
it is between x = 0 and x = +x m and is traveling toward x = -x m
it is between x = 0 and x = -x m and is traveling toward x = -x m
t=
Ans:
𝐁
t=
3T
4
T
2
−xm
Q2:
t=0
+xm
x
A 1 kg object is attached to an ideal spring (k = 100 N/m) and is oscillating on a
horizontal frictionless surface. The displacement of the object is given by x(t) =
x m cos(ωt + φ). The object is initially displaced by a distance of 5 cm from the
equilibrium position and then released. Find the speed (in m/s) of the object after 3
seconds if the phase constant φ = 360o.
Ans:
VH =
dx
= −ωxm sin(ωt + φ)
dt
Speed = |v| = |ωxm sin(ωt + φ)|where ω = �
k
100
= �
= 10 rad/s
m
1
So speed = |10 × 0.05 sin(10 × 3 + 2π)| = 0.494 m/s
Q3:
An ideal spring is attached to the wall at one end and to a block of mass m =2 kg at
the other end. The block can oscillate on a horizontal frictionless surface. The block
has a kinetic energy of 5 J and the spring has a potential energy of 4 J when the block
is at certain distance x from the equilibrium position. Find the speed (in m/s) of the
block when it passes by the equilibrium position x = 0.
Ans:
Conservation of Mechanical equation:
k i + Ui = k f + Uf
at equilibrium
k i + Ui =
1
2
mv 2 ⇒ V = � (k i + Ui )
2
m
2
⇒ v = � (5 + 4) = √9 = 3.00m/s
2
KFUPM-Physics Department
1