let position at any time be given as
x(t)=A*sin(w*t)
where A=amplitude=0.15 m
w=angular frequency=2*pi/period=2*pi/0.45=13.963 rad/sec
hence x(t)=0.15*sin(13.963*t) m
veloicty=dx/dt=0.15*13.963*cos(13.963*t)=2.0944*cos(13.963*t)
m/s
as angular frequency=sqrt(spring constant/mass)
==>13.963=sqrt(spring constant/0.3)
==>spring constant=13.963^2*0.3=58.49 N/m
a)
when the mass passes through equilibrium, x(t)=0
==>w*t=0
at that time, speed=2.0944*cos(0)=2.0944 m/s
part b:
as there is no friction, total energy of the system will be
conserved.
at the highest displacement point, speed of the mass is 0.
then total energy of the system=potential energy of the
spring=0.5*spring cosntant*amplitude^2
=0.5*58.49*0.15^2=0.658 J
part c:
spring constant is 58.49 N/m
part d:
acceleration of the mass=dv/dt=-2.0944*13.963*sin(13.963*t)
as maximum value of sine function is 1,maximum
acceleration=2.0944*13.963=29.244 m/s^2
