Two springs with spring constants k1 and k1 are connected toeach
other in series, end to end. The top of the first spring isattached to the ceiling and the second
string is connected and hanging below the first spring. A mass M isconnected to the bottom of
the second spring. The acceleration of gravity is g . Answer thefollowing in terms of quantities
given or a subset thereof.
(a) Derive an expression for the effective spring constant of thespring system?
(b) As the mass hangs vertically and sits motionless what is thedistance beyond equilibrium
that the system is stretched?
(c) What is the frequency of the small oscillations of thesystem?
(d) What is the period of the small oscillations.
(e) If the mass were doubled by what factor would the period of thesmall oscillations
change?
Two springs with spring constants k1 and k1 are connected toeach
other in series, end to end. The top of the first spring isattached to the ceiling and the second
string is connected and hanging below the first spring. A mass M isconnected to the bottom of
the second spring. The acceleration of gravity is g . Answer thefollowing in terms of quantities
given or a subset thereof.
(a) Derive an expression for the effective spring constant of thespring system?
(b) As the mass hangs vertically and sits motionless what is thedistance beyond equilibrium
that the system is stretched?
(c) What is the frequency of the small oscillations of thesystem?
(d) What is the period of the small oscillations.
(e) If the mass were doubled by what factor would the period of thesmall oscillations
change?
