[Analog_Engine.git] / scripts / TP1 10.28 Masses hanging on springs.LACE

# TP1 10.28 Masses hanging on springs
# Two identical masses m are hanging on 2 springs with same spring constant D. The system is performing small oscillations around the equilibrium position.
# m*s1'' + D*s1 + D*(s1-s2) = 0 => s1'' = D/m * (s2 - 2*s1) = D/m*s2 - D/m*s1 - D/m*s1
# m*s2'' + D*(s2-s1) = 0        => s2'' = D/m * (s1 - s2) = D/m*s1 - D/m*s2

coefficient(1): D/m_1 # D/m for s1
coefficient(2): D/m_2 # D/m for s2, identical to D/m_1
coefficient(3): -1 -> -s1_0 # initial position of s1
coefficient(4): -1 -> -s2_0 # initial position of s2

iintegrate D/m*s2, -D/m*s1, -D/m*s1 -> -s1' # input is s1''
iintegrate -s1' -> s1
   IC: -s1_0
s1 * D/m_1 -> D/m*s1
invert D/m*s1 -> -D/m*s1

iintegrate D/m*s1, -D/m*s2 -> -s2' # input is s2''
iintegrate -s2' -> s2
   IC: -s2_0
s2 * D/m_2 -> D/m*s2
invert D/m*s2 -> -D/m*s2

output(x): s1
output(y): s2
Commit	Line	Data
56968557 P	1	# TP1 10.28 Masses hanging on springs
	2	# Two identical masses m are hanging on 2 springs with same spring constant D. The system is performing small oscillations around the equilibrium position.
	3	# ms1'' + Ds1 + D(s1-s2) = 0 => s1'' = D/m (s2 - 2s1) = D/ms2 - D/ms1 - D/ms1
	4	# ms2'' + D(s2-s1) = 0 => s2'' = D/m * (s1 - s2) = D/ms1 - D/ms2
	5
	6	coefficient(1): D/m_1 # D/m for s1
	7	coefficient(2): D/m_2 # D/m for s2, identical to D/m_1
	8	coefficient(3): -1 -> -s1_0 # initial position of s1
	9	coefficient(4): -1 -> -s2_0 # initial position of s2
	10
	11	iintegrate D/ms2, -D/ms1, -D/m*s1 -> -s1' # input is s1''
	12	iintegrate -s1' -> s1
	13	IC: -s1_0
	14	s1 * D/m_1 -> D/m*s1
	15	invert D/ms1 -> -D/ms1
	16
	17	iintegrate D/ms1, -D/ms2 -> -s2' # input is s2''
	18	iintegrate -s2' -> s2
	19	IC: -s2_0
	20	s2 * D/m_2 -> D/m*s2
	21	invert D/ms2 -> -D/ms2
	22
	23	output(x): s1
	24	output(y): s2