A body of mass 1kg is attached to a wall by a spring with k1

A body of mass .1kg is attached to a wall by a spring with k=15N/m. It is initially pulled a distance of x = .2m from its equilibrium position and released from rest. a. What is its initial PE? b. What is its initial KE? c. What is its total energy? d. What is the velocity when it passes through the equilibrium position? e. What are the (i) amplitude (ii) frequency (iii) period of motion (iv) angular frequency?

Solution

a)

Initial Potential energy

U=(1/2)Kx²=(1/2)*15*0.2²=0.3 J

b)

initial Kinetic energy

KE_initial=0 (since it starts from rest)

c)

total energy

E=0.3 J

d)

=>(1/2)mV²=0.3

(1/2)*0.1*V²=0.3

V=2.45 m/s

e)

amplitude

A=0.2 m

angular frequency

w=sqrt(K/m)=sqrt(15/0.1)=12.25 rad/sec

frequency

f=W/2pi =12.28/2pi=1.95 Hz

period of motion

T=1/f=1/1.95=0.513 sec